Derivatives

Polynomials and Exponential functions

100

Find y'

3²⁰

0

200

Find y'

9x+3

9

300

Find y'

3x³ +5x² +x + 23

9x² +10x + 1

400

Find y"

x^1/2 - 3x²

-1/4x^-3/2 - 6

500

Find y'

5^x

ln(5)5^x

Products and Quotients

100

Find y' 

x² * e^x

e^xx² +2xe^x

200

Find y'

(2+2x)/3x²

(6x² - (12x + 12x² )) / 9x⁴

300

Find y'

(x² +x)(4x³ +2x² +6)

(x²+x)(12x² + 4x) +(2x+1)(4x³ +2x² +6)

400

Find y'

(x³ +4x)/ (2x² + 5x +2)

((2x² + 5x +2)(3x² +4) - (x³ +4x)(4x + 5)) /  (2x² + 5x +2)²

500

Find y" 

(x³ +4x)/ (2x² + 5x +2)

(10(5x³ -8x² -8)) / (5x +2x² +2)³

Chain rule

100

Find y' 

e^2x

2e^2x

200

Find y'

sin(2x)

2cos(2x)

300

Find y' 

e^cos(x)

-sin(x)e^cos(x)

400

Find y'

(4x⁸ + 3x³)⁵

(160x⁷ + 45x² )(4x⁸ + 3x³)⁴