Basic Integrals

Basic

100

3

What is the derivative of 3x+C ?

200

2x+1

What is the derivative of x²+2x+C ?

300

1/x

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

400

e^x

What is the derivative of e^x+C ?

500

0

What is the derivative of a constant (C) ?

Basic Trigonometric

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

-csc(x)cot(x)

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

Polynomials

100

3x²+6x-7

What is the derivative of x³+3x²-7x+C ?

200

x+3/2

What is the derivative of (1/2)x²+(3/2)x+C ?

300

x³+7x+5

What is the derivative of (1/4)x⁴+(7/2)x²+5x+C ?

400

3x(x+4)

What is the derivative of x³+6x²+C ?

500

7x⁶+10x⁴-12x³+36x²

What is the derivative of x⁷+2x⁵-3x⁴+12x³+C ?

Log/Exponential

100

2e^2x

What is the derivative of e^2x+C ?

200

2/x

What is the derivative of 2lnx+C ?

300

-4e^-2x

What is the derivative of 2e^-2x+C ?

400

1/(x+1)

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

500

ln(2)

What is the derivative of ln(2)x+C ?  ln(2) is just a CONSTANT!!!

Roots

100

(3/2)x^1/2

What is the derivative of x^3/2+C ?

200

(1/2)x ^-(1/2)

What is the derivative of x^1/2+C ?

300

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

What is the derivative of (2x+3)^1/2+C ?

400

10x^(3/2)

What is the derivative of 4x^(5/2)+C ?

500

-6x ^-(3/2)

What is the derivative of 12x ^-(1/2)+C ?