Chapter 3 Quiz 2 Review

Trig

100

Derivative of y=cosx

What is y'=-sinx

200

Derivative of y=8sinx+tanx

What is y'=8cosx+sec²x

300

Derivative of y=-cscx

What is y'=cotxcscx

400

Derivative of y=cot(secx)

What is y'=-csc²(secx)tanxsecx

500

Derivative of y=tan³x-cos²(3x)

What is y'=3tan²xsec²x+6cos(3x)sin(3x)

Chain Rule

100

Derivative of y=(3x+4)²

What is y'=6(3x+4)

200

Derivative of y=sin²(11x)

What is y'=22sin(11x)cos(11x)

300

Derivative of y=(3x²+5x-2)⁸

What is y'=8(6x+5)(3x²+5x-2)⁷

400

Derivative of y=(5x²+3x-1)^1/2

What is y'=(10x+3)/(2(5x²+3x-1)^1/2)

500

Find the slope of the tangent line to the curve y=(x²-3)⁵ at x=-1

What is y'(-1)/m=-160

Implicit

100

Derivative of x²+y²=25

What is dy/dx=-x/y

200

Derivative of y=sinx+cosy

What is dy/dx=(cosx)/(1+siny)

300

Derivative of x²-xy+y²=3

What is dy/dx=(y-2x)/(2y-x)

400

Derivative of x²y+y⁴=4+2x

What is dy/dx=(2-2xy)/(x²+4y³)

500

Derivative of x²y³-xy=10

What is dy/dx=(2xy³-y)/(x-3x²y²)

Inverse Trig

100

Derivative of y=csc^-1x

What is y'=-1/(|x|(x²-1)^1/2)

200

Derivative of y=4sin^-1x

What is y'=4/(1-x²)^1/2

300

Derivative of y=cos^-1(5x)

What is y'=-5/(1-25x²)^1/2

400

Derivative of y=tan^-1(x^3/2)

What is y'=(3(x^1/2))/(2(1+x³))

500

Derivative of y=(cos^-1(4x²))²

What is y'=(-16xcos^-1(4x²))/(1-16x⁴)^1/2

Exponential and Log

100

Derivative of y=e^-6x

What is y'=-6e^-6x

200

Derivative of y=12ln(x²)

What is y'=24/x

300

Derivative of y=2^sinx

What is y'=ln2(cosx)2^sinx

400

Derivative of y=log₃(7x)

What is y'=1/(xln3)

500

Find the slope of the tangent line to the curve y=(15e^4x)² for any value of x

What is y'/m=1800e^8x