Antiderivative Review

Trigonometric Functions

100

cos(x) 

What is the derivative of sin(x) + C?

200

sin(x)

What is the derivative of -cos(x)+C ?

300

sec²(x)

What is the derivative of tan(x)+C ?

400

sec(x)tan(x)

What is the derivative of sec(x) + C?

500

csc²(x)

What is the derivative of -cot(x) + C ?

Polynomials

100

2x

what is the derivative of x²+C ?

200

-x²

What is the derivative of -(1/3)x³ + C?

300

4x³

What is the derivative of x⁴ + C ?

400

3x¹⁷

What is the derivative of (3/18)x¹⁸ + C OR (1/6)x¹⁸+C

500

x^-4

What is the derivative of -(1/3)x^-3 + C ?

log functions

100

1/x

What is the derivative of ln|x| + C ?

200

1/(x-1)

What is the derivative of ln|x-1| + C ?

300

1 / (2-x)

What is the derivative of -ln|2-x| + C ?

400

(1 / cos(x)) * sin(x)

What is the derivative of -ln|cosx| + C ?

500

1 / (x * ln2)

What is the derivative of  ln(|x|)/ln2 +C OR log₂(|x|) + C ?

e^xExponential

100

e^x

What is the derivative of e^x + C?

200

3e^x

What is the derivative of 3e^x + C?

300

e^4x

What is the derivative of (1/4)e^4x+C ?

400

2e^-2x

What is the derivative of -e^-2x + C?

500

-(1/3)e^-3x

What is the derivative of (1/9)e^-3x + C ?

Root functions

100

1/(2√x)

What is the derivative of √x + C?

200

(1/3)x^-2/3

What is the derivative of x^1/3 + C ?

300

x^2/5

What is the derivative of (5/7)x^7/5 + C?

400

cos(√x)*(1 / (2√x))

What is the derivative of sin(√x) + C ?

500

1 / (2x)

What is the derivative of (1/2)ln(|x|) + C ?