SIMPLE DERIVATIVES

Polynomials

100

What is the derivative of y = 3x² ?

y' = 6x

200

Find the derivative of f(x) = 5

0

300

Find the derivative of f(x) = 6x³ + x - 2

18x² + 1

400

Find the derivative of y=-2/(x⁷).

y'=14x^-8

500

Find the derivative of g(x)=2x^1/2.

g'(x)=x^-1/2

Product

100

What is the derivative of (x-2)(x³+3)

4x³-6x²+3

200

What is the derivative of (x²+3)(x-2)

3x²-4x+3

300

What is the derivative of (x²)(x³+2x)

5x⁴+6x²

400

What is the derivative of (x²+3)(x²-4)

4x³-2x

500

What is the derivative of (2x⁷+3)(x³-4)

20x⁹-52x⁶+9x²

Quotient

100

What is the derivative of 5/(x-1)

-5/(x-1)²

200

What is the derivative of 5x/(x+1)

5/(x+1)²

300

What is the derivative of 5x²/(x+1)

(5x²+10)/(x+1)²

400

What is the derivative of 5x²/(x²+1)

10x/(x²+1)²

500

What is the derivative of (x²-1)/(x²+1)

4x/(x²+1)²

Trigonometric

100

Find the derivative of y=sin(x).

y'=cos(x)

200

What is the derivative of f(t)=cos(t)?

f'(t)=-sin(t)

300

Find the derivative of y=-tan(x).

y'=-sec²(x)

400

What is the derivative of y=csc(x)?

y'=-csc(x)cot(x)

500

What is the derivative of y=-1/6 cot(x)?

y'=1/6 csc²(x)

Log/Exponential

100

What is the derivative of h(x)=x²e^x?

h'(x)=2xe^x+x²e^x

200

What is the derivative of y=e^2x?

y'=2e^2x

300

What is the derivative of ln(2x²)

2/x

400

What is the derivative of ln(4x³)

3/x

500

What is the derivative of Log₁₂2x³

3/x ln(12)