1. Answer: 1/2 <span>Find the slope of the graph of the relation x^2y + 4y = 8 at the point (2, 1). In exponent graph, the slope will be constantly changed so you need to determine a fixed point. The slope in point 2,1 would be: m= y/x= 1/2
2. Answer: </span>-csc(y) <span>Find y' if x = cos(y) </span> x = cos(y)<span> dx = -sin(y)dy dy/dx = -1/sin(y) </span>dy/dx = -csc(y) <span>y' = -csc(y)</span><span>
3. Answer: </span>y''= -0.48 <span>If 2x^2 + y^2 = −2 then evaluate d^2y/dx^2 when x = 2 and y = 3. Round your answer to 2 decimal places. </span> First you need differentiate the equation implicitly 2x^2 + y^2 = −2 dy/dx= 2*2 x^(2-1) + 2*y^2-18y' 4x+4y'y=0 4y'y=-4x y'= -x/y
Then find out the y'' using quotient differentiation y'= -x/y y''=<span>(−y + xy')/y²
4. answer = 2( x+1) ^(2) Find dy/dx if f(x) = (x + 1)^2x. In this question, the number is (x+1) power 2x. You don't need to touch the (x+1). Just do the differentiation focusing on the 2x. y= (x + 1)^2x dx/dy= 2*( x+1)^(1*2 x^1-1) dx/dy= 2( x+1) ^(2)