Derivative Practice for Advanced

Calculus (Quotient Rule)

100

Find the derivative of: y = 

(-3(3x - 2x^2))/(7x)

What is: y'= 

6/7

200

Find the derivative of : y= xrootx

What is : y' = (3rootx)/2

300

Find the derivative of:  y= 

(x^2)/(2sqrtx + 1

What is: y' = 

(x(3sqrtx + 2))/(2sqrtx + 1)^2

400

Find the slope of the normal to the curve y = x^2 +3x - 2 at (4,7).

 f(x)= 

What is: 

-1/11

Calculus (Chain Rule)

100

Find the derivative of:

𝑓⁡(𝑥) =[𝑔⁡(𝑥)]𝑛

𝑓′⁡(𝑥)=𝑛⁢[𝑔⁡(𝑥)]^(𝑛−1)⁢𝑔′⁡(𝑥)  

200

f(t)=sqrt(1-t)

f'(t)=-1/(2(1-t)^1/2)

300

s(t)=1/(t^2+3t-1)

(-2t-3)/(t^2+3t-1)^2

400

y=(2x-7)^3

y'=6(2x-7)^2

Calculus (Product Rule)

100

Find the derivative of: 𝑓⁡(𝑥) =(6⁢(𝑥^3)−𝑥)⁢(10−20⁢𝑥)

f'(x) = −480(⁢𝑥^3)+180(⁢𝑥^2)+40⁢𝑥−10 

200

Find the derivative of:  y=(3x-2x²)(5 + 4x)

What is:  y' = -24x² +4x + 15.

300

Find y'(2), if : y = (x - 4)(x² + 6x -1)

What is: -5

400

Find the derivative of the function: 𝑓⁡(𝑥) =4/(𝑥^6) 

𝑓′⁡(𝑥)=−24⁢(𝑥^−7)