Derivatives

Trig

100

sin (x)

cos (x)

200

tan (x)

sec² (x)

300

sec (x) + csc (x)

sec (x) tan (x) - csc (x) cot (x)

400

tan^-1 (x)

1 / 1 + x²

500

sin^-1 (x)

1 / sqrt (1 - x²)

Power rule

100

4x³ 

12x²

200

6x

6

300

9x⁵

45x⁴

400

5x³ + 3x⁵ - 15x

15x² + 15x⁴ - 15

500

4 / x²

- 8 / x³

Potpouri

100

e^4x

4e^4x

200

ln (x) 

1 / x

300

3^x

ln (3) 3^x

400

ln (2x²)

2 / x (or 4x / 2x²)

500

sqrt (x² + 4)

x / sqrt (x² + 4)

Rules

100

Power rule

xⁿ

n x^n-1

200

Product rule  f(x) g(x)

f ' (x) g (x) + g ' (x) f (x)

300

Quotient rule   f (x) / g (x)

(f ' (x) g (x) + g ' (x) f (x)) / g² (x)

400

Chain rule   f ( g (x))

f ' (g (x)) g ' (x)

500

Golden rule

Treat others the way you want to be treated

Really Hard?

100

x⁴ - x³ + 2x² - 3x + 19

4x³ -3x² + 4x - 3

200

6 cos (-3x)

18 sin (-3x)

300

ln (3x⁴)

4 / x³   (or 12x³ / 3x¹²)

400

sqrt (7 - 2x)

- 1 / sqrt (7 - 2x)  (or - 2 / 2 sqrt (7 - 2x)

500

cos (x) / sin (x)  

- csc² (x)