AP Calculus Derivatives Practice

Product Rule

100

y=-x³(3x⁴-2)

-21x⁶+6x²

200

y=x²(-3x²-2)

-12x³-4x

300

f(x) = (2x⁴-3)(x²+1)

12x⁵+8x³-6x

400

y=(5x⁵+5)(-2x⁵-3)

-100x⁹-125x⁴

500

f(x) = (x⁴+3)(-4x⁵+5x⁴+5)

-36x⁸+40x⁷-60x⁴+80x³

Quotient Rule

100

f(x)=2/x⁵-5

f'(x)=-10x⁴/x¹⁰-10x⁵+25

200

f(x)= 5/4x³+4

f'(x)=-15x²/4x⁶+8x³+4

300

y=3x⁴+2/3x³-2

y'=9x⁶-24x³-18x²/9x⁶-12x³+4

400

y=x⁴+6/3-4x^-4

y'=12x¹¹-32x⁷-96x³/9x⁸-24x⁴+16

500

y=4x⁴-4x²+5/2x^5/3+3

y'=56x^14/3+144x³-8x^8/3-72x-50x^2/3/12x^10/3+36x^5/3+27

Chain Rule

100

y=(x²+4x+6)⁵

y'=5(2x+4)(x²+4x+6)⁴

200

f(x)=(x³-5x)⁴

f'(x)=4(3x²-5)(x³-5x)³

300

y=cos³(x)

y'=3sinxcos²x

400

y=(x-6 / x+7)³

y'=39(x-6)^2/(x+7)^4

500

y=sin³(2x+3)

y'=6cos(2x+3)sin²(2x+3)

Power Rule

100

y=5x¹⁸

f'(x)=90x¹⁷

200

f(x)=4x⁴-5x-3

f'(x)=16x³-5

300

y=3x^5/4

y'=15x^1/4/4

400

y=-4x^-5

y'=20/x⁶

500

y=3/x³

y'=9/x⁴

Anti-Derivatives

100

f(x)=-x+tanx

f'(x)=-1+sec²x

200

f(x)=sinxcosx

f'(x)=cos²x-sin²x

300

f(x)=2xsinx+x²cosx

f'(x)=4xcosx+2sinx-x²sinx

400

f(x)=sinx/x³

f'(x)=xcosx-3sinx/x⁴

500

f(x)=x⁵/4sinx

f'(x)=x⁴(5sinx-xcosx)/4sin²x