Mike’s Derivatives

Add/Sub/Power

100

y=3x²+6

dy/dx=6x

200

y=4x⁴-6x²

dy/dx=16x³-12x

300

y=x²+1

dy/dx=2x

400

y=4x⁵+3x³

dy/dx=20x⁴+9x²

500

y=2x⁵-2x

dy/dx=10x⁴-2

Chain Rule

100

y=(x+8)⁴

dy/dx=4(x+8)³

200

y=(5x⁴+5)^-5

dy/dx=-100x³/(5x⁴+5)⁶

300

y=(-3x⁴+6)²

dy/dx=-24x³(-3x⁴+6)

400

y=(4x+4)³

dy/dx=12(4x+4)²

500

(6x+3)^-4

dy/dx=-24/(6x+3)⁵

Quotient Rule

100

y=4/6x²+2

dy/dx=-48x/(6x²+2)²

200

y=6x⁴/4x⁵+5

dy/dx=-24x⁸+120x³/(4x⁵+5)²

300

y=8/4x³+3

dy/dx=-96x²/(4x³+3)²

400

y=12x²/x³+3

dy/dx=-12x⁴+72x/(x³+3)²

500

y=4x⁶/5x⁶+8

dy/dx=192x⁵/(5x⁶+8)²

Product Rule

100

y=(4x⁴+6)•6x²

dy/dx=144x⁵+72x

200

y=(x⁶+3)(2x²+4)

dy/dx=16x⁷+24x⁵+12x

300

y=(8x²-8)•10x²

dy/dx=320x³-160x

400

y=(-9x³+2)(-5x³+4)

dy/dx=270x⁵-138x²

500

y=4x³(3x²+2)

dy/dx=60x⁴+24x²

Implicit Differentiation

100

6=3x³+4y⁴

dy/dx=-9x²/16y³

200

5x=9y⁴+6

dy/dx=5/36y³

300

3=4x²-y⁴

dy/dx=2x/y³

400

9y²+2=4x³

dy/dx=2x²/3y

500

-y³+6x=9

dy/dx=2/y²