Derivative Shortcut Formulas

Random

100

x³

3x² 

200

e-arccos(x)

1/sqrt(1-x²)

300

6x^1/2

3x^-1/2 

400

3/4x^-9+4x-e^x

-27/4x^-10+4-e^x

500

(x²-1)²

2(x²-1)(2x)

Spicy

100

1/x

-1/x²

200

x/(x+1)

1/(x+1)²

300

(4x³+1)/2

6x²

400

(4x⁶+8x⁵+2x⁴)/2x⁵

12-1/(x²)

500

1/(4-x²)^1/2

(4-x²)^-3/2(x)

Figge's Favorite

100

sin(x)

cos(x)

200

-tan(x)

-sec²(x)

300

csc(x)

-cos(x)/(sin²(x))

400

cos²(x)+sin²(x)

0

500

(cot(x)*sin(x))²

-2cos(x)sin(x)

Chris' Favorite

100

-cos(2x)

2sin(2x)

200

3(5x+4)²

30(5x+4)

300

4(x³)¹⁰

120x²⁹

400

(5x²+1)^1/2

(5x²+1)^-1/2(5x)

500

sin(sin(sin(x)))

[cos(sin(sin(x)))]*[cos(sin(x))*cos(x)]

Simplify Answer

100

(x²)(x²)

4x³

200

(x-1)(3x+4)

6x+1

300

(1/3x²)(2x³)

10/3x⁴

400

(z³+4z²+z)(z-1)

4z³+9z²-6z-1

500

(t-2)³(ln(t))

(3t(t-2)²ln(t)+1)/t