One A
y = e^x
dy/dx = e^x The f(x) = the differentiated function. Any value that e^x can have, the derivative has the same value. x is contained in all the reals.
One B
y = x*e^x
y' = e^x + xe^x Using the multiplication rule.
You want the slope and the value of the of y to be the same. The slope is y' of the tangent line
xe^x = e^x + xe^x
e^x = 0
This happens only when x is very "small" like x = - 4444444
y = e^x * ln(x) Using the multiplication rule again, we need the slope of the line with is y'
y1 = e^x
y1' = e^x
y2 = ln(x)
y2' = 1/x
y' = e^x*ln(x) + e^x/x So at x = 1 the slope of the line =
y' = e^1*ln(1) + e^1/1
y' = e*0+e = e
y = mx + b
y = ex + b
to find b we use y= e^x ln(x)
e^x ln(x) = e*x + b
e^1 ln(1) = e*1 + b
ln(1) = 0
0 = e + b
b = - e
line equation and answer.
y = e*x - e
Answer:
D
Step-by-step explanation:
So it'd be
28=3s+4
28-4=3s
24=3s
24/3=3s/3
8=2
Answer:
One days trip of to school from home and back home from school is 2/3 of a mile. We want to know how far it is to school from her house.
To solve this, we simply need to take half of the total distance (2/3)
\frac{2}{3} / 2
Next, we need to turn the 2 into a fraction. Every whole number can be made into a fraction by putting it over 1.
\frac{2}{3} / \frac{2}{1}
Because we are dividing, we need to invert the second fraction and then multiply.
\frac{2}{3} * \frac {1}{2}
Next, we multiply the top of the first fraction by the top of the second and the bottom of the first fraction by the bottom of the second.
\frac{2}{6}
Once you reduce, you get:
\frac{1}{3}
Above step we use "Multiplication property of equality"
In the above step we "Simplify on both sides of equation"
In the above step we use "Distribution property"
The above step is the result of using "Subtraction property of equality"
Above step is result of "Combining the like terms"
Above step is the result of using "Division property of equality"
Above step is result of "Simplifying fractions on either side of equation"
