AP CALCULUS AB

Product Rule

100

y=(3x+10)(x²+x-4)

(3)(x²+x-4)+(2x+1)(3x+10)

200

f(x)=(1-7x³+9x)(-10+8x)

f`(x)=(-21x²+9)(-10+8x)+(8)(1-7x³+9x)

300

y=(2x²-3)(-5x²-6+10x^-1)

(4x)(-5x²-6+10x^-1)+(-10x-10x^-2)(2x²-3)

400

y=x³-xsinx

3x²-sinx-xcosx

500

f(X)=(2x+4+5x³)cosx

(2+15x²)(cosx)+(-sinx)(2x+4+5x³)

Chain Rule

100

(sin(4x-8))

4cos(4x-8)

200

f(x)=3(5x²+6)⁶

18(5x²+6)⁵(10x)

300

y=2sin²(2x³)

24x²sin(2x³)cos(2x³)

400

y=sin[(x+5)⁵]

5(x+5)⁴cos[(x+5)⁵]

500

f(x)=-3cos²(2-x)

-6cos(2-x)sin(2-x)

Quotient Rule

100

f(x)=(5+x²)/(2x²-1)

(-22x)/(2x²-1)²

200

f(x)=(2x³+3)/(1+x)

(4x³+6x²-3)/(1+x)²

300

f(x)=(5+4x²)/(3x-2)

(12x²-16x-15)/(3x-2)²

400

f(x)=(x)/(2-x²)

(x²+2)/(2-x²)²

500

f(x)=(x-1)/(1-3x³)

(6x³-9x²+1)/(1-3x³)²

Advanced Derivates

100

y=e^{2x^5+5x^4}

e^{2x^5+5x^4}(10x⁴+20x³)

200

y=ln(-3x⁵)

(1)/(-3x⁵)(-15x⁴)

300

y=log₇(7x⁶+9x⁵)

(1)/(7x⁶+9x⁵)ln7*(42x⁵+45x⁴)

400

if f(x)= -3x/e^-4x, then what is the value of f`(-2)?

(21)/(e⁸)

500

f(x)=12e^-2x-2. What is the equation of the line tangent to the graph of f when the slope of the tangent line is equal to -12?

y-4=-12(x-ln(2))/(2)

Advanced Derivates

100

if f(x)=ln(sqr(x)), what is the value of f`(3)?

1/6

200

what is the slope of the line tangent to the graph of y=ln(cos3x) at the point where x=7pi/12?

3

300

what is the slope of the line tangent to the graph of y=ln(x)/x at the point where x=1/sqr(e)?

3e/2

400

f(x)=cos^-1(x), what is the value of f`(sqr8/3)

-3

500

the function f is defined by f(x)=x³+4x+1. if g(x)=f^-1(x) and g(6)=1, what is the value of g`(6)?

1/7