Derivative Game

Product Rule

100

y= (9+3x)(2x)

y’=12x+18

200

y=(4x²+1)(2x-3)

y'=24x²-24x+2

300

y=7xsinx

y’=7sinx+7xcosx

400

y=-6xcosx+4xtanx

y'=6xsinx-6cosx+4xsec²x+4tanx

Quotient Rule

100

y=(x+1)/(4x⁴)

y'=(-3x-4)/(4x⁵)

200

y=8x/3x²

y’=(24x²-48x)/(3x²)²

300

y=(8x²+x³)/(4sinx)

y'=(16xsinx-9x³cosx+3x²sinx)/(4sin²x)

400

y=cot6x/sec9x

y’= (-sec9xcsc²6x-cot6xsec9xtan9x)/(sec9x)²

Chain Rule

100

y=4(3-2x²)³

y'=-48x(3-2x²)²

200

y=e^-x²+7x-10

y’=e^-x²+7x-10(-2x+7)

300

y=cot²(-13x+6)

y’=-26(cot(-13x+6))(-csc²(-13x+6))

Mixed

100

y=1/(4xsinx)

Use Product Rule

y’=-1(4xsinx)^-²(4cosx)

200

y= 4x((2x²)/(x²-4x))

y'= 4x ((-16x²+8x²)/(x²-4x)²) (8x²/(x²-4x))

300

y=(-4csc³x)(7x+5)

y'=-28csc³x+12csc³xcotx(7x+5)

400

y=((x²-9)/(x-1))⁵

Use Quotient Rule and chain and simplify

y’=5((x²-9)/(x-1))⁴((x²-2x+9)/((x-1)²)

The Basics

100

d/dx cosx

-sinx

200

d/dx secx

secxtanx

300

d/dx lnx

1/x

400

d/dx logbx

1/xlnb