Practice with Derivatives

What is the derivative of a constant, C?

• C

• 0

• 1

• You can't take the derivative of a constant.

Given the information below, find the value of h'(3).

h(x) = f(x)*g(x)

f(3) = 5

f'(3) = -2

f'(-10) = 2

g(3) = -10

g'(3) = 3

• 5

• $\frac{1}{20}$

• 35

• 6

• $\frac{1}{10}$

Tags

CCSS.HSF-BF.A.1C

Given the information below, find the value of h'(3).

h(x) = f(g(x))

f(3) = 5

f'(3) = -2

f'(-10) = 2

g(3) = -10

g'(3) = 3

• 5

• $\frac{1}{20}$

• 35

• 6

• $\frac{1}{10}$

Tags

CCSS.HSF-BF.A.1C

Given the information below, find the value of h'(3).

h(x) =  $\frac{f\left(x\right)}{g\left(x\right)}$  

f(3) = 5

f'(3) = -2

f'(-10) = 2

g(3) = -10

g'(3) = 3

• 5

• $\frac{1}{20}$

• 35

• 6

• $\frac{1}{10}$

Tags

CCSS.HSF-BF.A.1B

What is the slope of the line tangent to f(x) = $e^x\cos\ x$  at x = 0?

• 0

• 1

• e

• 2e

Write the equation of the line tangent to f(x) at x = 3.
 $f\left(x\right)\ =\ \sqrt{x^2-5}$  

•  $y\ -2\ =\ \ \frac{3}{2}\left(x-3\right)$  

•  $y\ -2\ =\ \ \frac{1}{4}\left(x-3\right)$  

•  $y\ -3\ =\ \ \frac{1}{4}\left(x-2\right)$  

•  $y\ -2\ =\ \ \frac{1}{6}\left(x-3\right)$  

•  $y\ -3\ =\ \ \frac{3}{2}\left(x-2\right)$  

Remember velocity is the derivative of position. If the position at seconds is given by s(t) . What is the velocity at 10 seconds?

 $s\left(t\right)\ =\ \frac{5t^{2\ }-\ 100}{2t-10}$  

• 200

• 20

• 1000

• 2

• 10

Remember acceleration is the second derivative of position. If the position at seconds is given by s(t) . What is the acceleration at 10 seconds?

 $s\left(t\right)\ =\ 5t^{2\ }-\ 100$  

• 500

• 50

• 1000

• 5

• 10

 $f\left(x\right)\ =\ \frac{e^x\ \left(5x+10\right)^2}{x}$  

Find f'(x)