Basic Derivatives
Product
Quotient Rule
Chain Rule
Mixed Bag
100
What is the derivative of y = 3x2 ?
y' = 6x
100
Find the derivative of y = 3x2 sin x
3x2 cos x + 6x sin x
100
Find the derivative of y = (5x - 2)/(x2 + 1)
(-5x2 + 4x + 5)/(x2 + 1)2
100

f(x)=cos2(x)

What is the outer function? What is the inner function? 

Outer: (  )2

Inner: cosx

100

Find the slope of the line tangent to f(x)=−3cos(3x) at x=pi/3

f′(x)=9sin(3x)
f'(pi/3)=0

200
Find the derivative of f(x) = 5
0
200
f(x) = (3x - 2x2)(5 + 4x)
-24x2 + 4x + 15
200
Find the derivative of f(x) = (2x + 5)/(x)1/2
(2x - 5)/(2x3/2)
200
Find y' if y = (3x - 9)4
12(3x - 9)3
200

Find equation for the slope of the line tangent to y=2cot2(x)

y'=−4cot(x)csc2(x) 

300
Find the derivative of f(x) = 6x3 + x - 2
18x2 + 1
300

Given the function f(x)=(8−7x3)(−5x3−7−3x2), find f′(x) in any form. 

f'(x)=(−21x2)(−5x3−7−3x2)+(−15x2−6x)(8−7x3)

300

y= (1+x2)/(2x2+3)

y'=(2x)/(2x2+3)2

300
Find the derivative of f(x) = sin 4x
4 cos 4x
300

Given the function y=4x3−4xcosx, find y' in any form.

y'=12x2−4cosx+4xsinx 

400
Find the derivative of f(x) = 3sinx - 2cosx
3cosx + 2sinx
400

Given the function f(x)=(3x3−4x)sinx, find f′(x) in any form.

f′(x)=(9x2−4)(sinx)+(cosx)(3x3−4x)

400

y=sinx/(1-2x)

y'=((1-2x)cosx+2sinx)/(1-2x)2

400
Find y' if y = (9x2 + 4)1/3
(6x)/(9x2 + 4)2/3
400

For the function f(x)=x2+8, find the equation of the tangent line at x=−5.

y−33=−10(x+5)

500

Find the derivative of f(x)=2cosx-5cotx

f'(x)=-2sinx+5csc2x

500

y=radical(x)cosx, y'=

No negative exponents, no rational exponents. 

y'=(1/2x−1/2)(cosx)−(sinx)(x1/2) 

500

y=tanx/secx

Write in SIMPLEST form.  Use those trig identities!!

y'=(sec3x-secxtan2x)/sec2x


y'=cosx

500
f(x) = sin3 4x Find f'(x)
12sin2 4x cos 4x
500

Given f(x)=3cos⁡(x), write the equation of the line tangent toy=f(x) when x=π/6.

y=-(3/2)(x-pi/6)+(3rad(3)/2)

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