Answer:
1/6
Step-by-step explanation:
Answer:
2x² + 4x
Step-by-step explanation:
= (3 - 1)(x + 2)(x)
= (2)(x + 2)(x)
= (2x + 4)(x)
= 2x² +4x
Differentiate both sides of the equation.<span><span><span>d<span>dx</span></span><span>(<span>x3</span>+<span>y3</span>)</span>=<span>d<span>dx</span></span><span>(18xy)</span></span><span><span>d<span>dx</span></span><span>(<span>x3</span>+<span>y3</span>)</span>=<span>d<span>dx</span></span><span>(18xy)</span></span></span>Differentiate the left side of the equation.Tap for fewer steps...By the Sum Rule, the derivative of <span><span><span>x3</span>+<span>y3</span></span><span><span>x3</span>+<span>y3</span></span></span> with respect to <span>xx</span> is <span><span><span>d<span>dx</span></span><span>[<span>x3</span>]</span>+<span>d<span>dx</span></span><span>[<span>y3</span>]</span></span><span><span>d<span>dx</span></span><span>[<span>x3</span>]</span>+<span>d<span>dx</span></span><span>[<span>y3</span>]</span></span></span>.<span><span><span>d<span>dx</span></span><span>[<span>x3</span>]</span>+<span>d<span>dx</span></span><span>[<span>y3</span>]</span></span><span><span>d<span>dx</span></span><span>[<span>x3</span>]</span>+<span>d<span>dx</span></span><span>[<span>y3</span>]</span></span></span>Differentiate using the Power Rule which states that <span><span><span>d<span>dx</span></span><span>[<span>xn</span>]</span></span><span><span>d<span>dx</span></span><span>[<span>xn</span>]</span></span></span> is <span><span>n<span>x<span>n−1</span></span></span><span>n<span>x<span>n-1</span></span></span></span> where <span><span>n=3</span><span>n=3</span></span>.<span><span>3<span>x2</span>+<span>d<span>dx</span></span><span>[<span>y3</span>]</span></span><span>3<span>x2</span>+<span>d<span>dx</span></span><span>[<span>y3</span>]</span></span></span>Evaluate <span><span><span>d<span>dx</span></span><span>[<span>y3</span>]</span></span><span><span>d<span>dx</span></span><span>[<span>y3</span>]</span></span></span>.Tap for more steps...<span><span>3<span>x2</span>+3<span>y2</span><span>d<span>dx</span></span><span>[y]</span></span><span>3<span>x2</span>+3<span>y2</span><span>d<span>dx</span></span><span>[y]</span></span></span>Differentiate the right side of the equation.Tap for fewer steps...Since <span>1818</span> is constant with respect to <span>xx</span>, the derivative of <span><span>18xy</span><span>18xy</span></span> with respect to <span>xx</span> is <span><span>18<span>d<span>dx</span></span><span>[xy]</span></span><span>18<span>d<span>dx</span></span><span>[xy]</span></span></span>.<span><span>18<span>d<span>dx</span></span><span>[xy]</span></span><span>18<span>d<span>dx</span></span><span>[xy]</span></span></span>Differentiate using the Product Rule which states that <span><span><span>d<span>dx</span></span><span>[f<span>(x)</span>g<span>(x)</span>]</span></span><span><span>d<span>dx</span></span><span>[f<span>(x)</span>g<span>(x)</span>]</span></span></span> is <span><span>f<span>(x)</span><span>d<span>dx</span></span><span>[g<span>(x)</span>]</span>+g<span>(x)</span><span>d<span>dx</span></span><span>[f<span>(x)</span>]</span></span><span>f<span>(x)</span><span>d<span>dx</span></span><span>[g<span>(x)</span>]</span>+g<span>(x)</span><span>d<span>dx</span></span><span>[f<span>(x)</span>]</span></span></span> where <span><span>f<span>(x)</span>=x</span><span>f<span>(x)</span>=x</span></span> and <span><span>g<span>(x)</span>=y</span><span>g<span>(x)</span>=y</span></span>.<span><span>18<span>(x<span>d<span>dx</span></span><span>[y]</span>+y<span>d<span>dx</span></span><span>[x]</span>)</span></span><span>18<span>(x<span>d<span>dx</span></span><span>[y]</span>+y<span>d<span>dx</span></span><span>[x]</span>)</span></span></span>Rewrite <span><span><span>d<span>dx</span></span><span>[y]</span></span><span><span>d<span>dx</span></span><span>[y]</span></span></span> as <span><span><span>d<span>dx</span></span><span>[y]</span></span><span><span>d<span>dx</span></span><span>[y]</span></span></span>.<span><span>18<span>(x<span>d<span>dx</span></span><span>[y]</span>+y<span>d<span>dx</span></span><span>[x]</span>)</span></span><span>18<span>(x<span>d<span>dx</span></span><span>[y]</span>+y<span>d<span>dx</span></span><span>[x]</span>)</span></span></span>Differentiate using the Power Rule which states that <span><span><span>d<span>dx</span></span><span>[<span>xn</span>]</span></span><span><span>d<span>dx</span></span><span>[<span>xn</span>]</span></span></span> is <span><span>n<span>x<span>n−1</span></span></span><span>n<span>x<span>n-1</span></span></span></span> where <span><span>n=1</span><span>n=1</span></span>.<span><span>18<span>(x<span>d<span>dx</span></span><span>[y]</span>+y⋅1)</span></span><span>18<span>(x<span>d<span>dx</span></span><span>[y]</span>+y⋅1)</span></span></span>Multiply <span>yy</span> by <span>11</span> to get <span>yy</span>.<span><span>18<span>(x<span>d<span>dx</span></span><span>[y]</span>+y)</span></span><span>18<span>(x<span>d<span>dx</span></span><span>[y]</span>+y)</span></span></span>Simplify.Tap for more steps...<span><span>18x<span>d<span>dx</span></span><span>[y]</span>+18y</span><span>18x<span>d<span>dx</span></span><span>[y]</span>+18y</span></span>Reform the equation by setting the left side equal to the right side.<span><span>3<span>x2</span>+3<span>y2</span>y'=18xy'+18y</span><span>3<span>x2</span>+3<span>y2</span>y′=18xy′+18y</span></span>Since <span><span>18xy'</span><span>18xy′</span></span> contains the variable to solve for, move it to the left side of the equation by subtracting <span><span>18xy'</span><span>18xy′</span></span> from both sides.<span><span>3<span>x2</span>+3<span>y2</span>y'−18xy'=18y</span><span>3<span>x2</span>+3<span>y2</span>y′-18xy′=18y</span></span>Since <span><span>3<span>x2</span></span><span>3<span>x2</span></span></span> does not contain the variable to solve for, move it to the right side of the equation by subtracting <span><span>3<span>x2</span></span><span>3<span>x2</span></span></span> from both sides.<span><span>3<span>y2</span>y'−18xy'=−3<span>x2</span>+18y</span><span>3<span>y2</span>y′-18xy′=-3<span>x2</span>+18y</span></span>Factor <span><span>3y'</span><span>3y′</span></span> out of <span><span>3<span>y2</span>y'−18xy'</span><span>3<span>y2</span>y′-18xy′</span></span>.Tap for fewer steps...Factor <span><span>3y'</span><span>3y′</span></span> out of <span><span>3<span>y2</span>y'</span><span>3<span>y2</span>y′</span></span>.<span><span>3y'<span>(<span>y2</span>)</span>−18xy'=−3<span>x2</span>+18y</span><span>3y′<span>(<span>y2</span>)</span>-18xy′=-3<span>x2</span>+18y</span></span>Factor <span><span>3y'</span><span>3y′</span></span> out of <span><span>−18xy'</span><span>-18xy′</span></span>.<span><span>3y'<span>(<span>y2</span>)</span>+3y'<span>(−6x)</span>=−3<span>x2</span>+18y</span><span>3y′<span>(<span>y2</span>)</span>+3y′<span>(-6x)</span>=-3<span>x2</span>+18y</span></span>Factor <span><span>3y'</span><span>3y′</span></span> out of <span><span>3y'<span>y2</span>+3y'<span>(−6x)</span></span><span>3y′<span>y2</span>+3y′<span>(-6x)</span></span></span>.<span><span>3y'<span>(<span>y2</span>−6x)</span>=−3<span>x2</span>+18y</span><span>3y′<span>(<span>y2</span>-6x)</span>=-3<span>x2</span>+18y</span></span>Divide each term by <span><span><span>y2</span>−6x</span><span><span>y2</span>-6x</span></span> and simplify.Tap for fewer steps...Divide each term in <span><span>3y'<span>(<span>y2</span>−6x)</span>=−3<span>x2</span>+18y</span><span>3y′<span>(<span>y2</span>-6x)</span>=-3<span>x2</span>+18y</span></span> by <span><span><span>y2</span>−6x</span><span><span>y2</span>-6x</span></span>.<span><span><span><span>3y'<span>(<span>y2</span>−6x)</span></span><span><span>y2</span>−6x</span></span>=−<span><span>3<span>x2</span></span><span><span>y2</span>−6x</span></span>+<span><span>18y</span><span><span>y2</span>−6x</span></span></span><span><span><span>3y′<span>(<span>y2</span>-6x)</span></span><span><span>y2</span>-6x</span></span>=-<span><span>3<span>x2</span></span><span><span>y2</span>-6x</span></span>+<span><span>18y</span><span><span>y2</span>-6x</span></span></span></span>Reduce the expression by cancelling the common factors.Tap for more steps...<span><span>3y'=−<span><span>3<span>x2</span></span><span><span>y2</span>−6x</span></span>+<span><span>18y</span><span><span>y2</span>−6x</span></span></span><span>3y′=-<span><span>3<span>x2</span></span><span><span>y2</span>-6x</span></span>+<span><span>18y</span><span><span>y2</span>-6x</span></span></span></span>Simplify the right side of the equation.Tap for more steps...<span><span>3y'=−<span><span>3<span>(<span>x2</span>−6y)</span></span><span><span>y2</span>−6x</span></span></span><span>3y′=-<span><span>3<span>(<span>x2</span>-6y)</span></span><span><span>y2</span>-6x</span></span></span></span>Divide each term by <span>33</span> and simplify.Tap for fewer steps...Divide each term in <span><span>3y'=−<span><span>3<span>(<span>x2</span>−6y)</span></span><span><span>y2</span>−6x</span></span></span><span>3y′=-<span><span>3<span>(<span>x2</span>-6y)</span></span><span><span>y2</span>-6x</span></span></span></span> by <span>33</span>.<span><span><span><span>3y'</span>3</span>=−<span><span><span>3<span>(<span>x2</span>−6y)</span></span><span><span>y2</span>−6x</span></span>3</span></span><span><span><span>3y′</span>3</span>=-<span><span><span>3<span>(<span>x2</span>-6y)</span></span><span><span>y2</span>-6x</span></span>3</span></span></span>Reduce the expression by cancelling the common factors.Tap for more steps...<span><span>y'=−<span><span><span>3<span>(<span>x2</span>−6y)</span></span><span><span>y2</span>−6x</span></span>3</span></span><span>y′=-<span><span><span>3<span>(<span>x2</span>-6y)</span></span><span><span>y2</span>-6x</span></span>3</span></span></span>Simplify the right side of the equation.Tap for more steps...<span><span>y'=−<span><span><span>x2</span>−6y</span><span><span>y2</span>−6x</span></span></span><span>y′=-<span><span><span>x2</span>-6y</span><span><span>y2</span>-6x</span></span></span></span>Replace <span><span>y'</span><span>y′</span></span> with <span><span><span>dy</span><span>dx</span></span><span><span>dy</span><span>dx</span></span></span>.<span><span><span>dy</span><span>dx</span></span>=−<span><span><span><span>x2</span>−6y</span><span><span>y2</span>−6x</span></span></span></span>
A vertical line on a sheet of lined graph paper is a vertical axis (normally called the X axis) that denotes everything to the left of the line is negative and everything to the right is positive. A horizontal line on that graph paper (normally called the Y axis) denotes everything below the line is negative and every thing above is positive. Each axis is graduated in scale. The equation X=Y has no single answer, but we can plot a locus of points on your graph by assigning values to X ( or Y) and create a diagonal line which passes thru the origin (where the lines cross) that denotes all possible answers to the equation that exist within the limits of the graph paper. Every equation will plot a locus of points.
20(7.5*10^-2)
the *10^-2 means we move the decimal of 7.5 2 places to the left
20(.075)
=1.5
