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= x√x

What is : y' = (3√x)/2

300

Find the derivative of: y= 

(1 - cos x)/ sinx

What is: y'= csc²x - cscx cotx.   or

(1- cosx)/ sin^2 x

400

Find the derivative of:  y= 

(x^2)/(2sqrtx + 1

What is: y' = 

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

500

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

y=sin(cosx)

-cos(cosx)sinx

200

f(t)=√(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

500

y=sin(pi x)

y'=pi cos(pi x)

Calculus (Product Rule)

100

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

What is:  y' = -24x² +4x + 15.

200

Find the derivative of:  y= 3x²sin(4x).

What is: y'= 6x[sin(4x) + 2xcos(4x)]

300

Find the derivative of: y= sin x cos x

What is:  y'= cos²x - sin²x

400

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

What is: -5

500

Find the derivative of: y= x²cos x, at c = pi/6.

What is: y' = 

(pi*sqrt3)/6 - pi^2/72

Calculus (Anything)

100

Find the derivative of f(x) = [ cos(2x) ]²

What is: -4[cos(2x)](sin(2x))

200

Find the slope of f(x)= (5/x³) - 3(x²)- (1/x) at x = -1

What is -8?

300

Find the derivative of f(x) = sin²(4x)

What is 8 sin (4x) cos (4x)?

400

Find the derivative of:  f(x)= y=sin(tan 2x)

What is :  2cos(tan 2x)(sec²(2x))

or

[2cos(tan 2x)]/(cos²(2x))

500

The slope of the normal line to the curve y= (2x²) + 1 at (1,3) is

What is -1/4 ?