Derivatives!

Chain Rule

100

f(x)=(2x-1)²

What is f'(x)=8x-4?

200

f(x)=(1/3x-5)³ (don't need to foil)

What is f'(x)=(1/3x-5)²?

300

f(x)=(3x-4)^1/2

What is f'(x)=(3/2)(3x-4)^(-1/2)?

400

f(x)=6(4x-5)^-1/3

What is f'(x)=-8(4x-5)^-4/3?

500

f(x)=(sin(2x)-15)^(-7/10)​​​​

What is f'(x)=(-7/5)cos(2x)(sin(2x)-15)^(-17/10)?

Quotient/Product Rule

100

f(x)=(2x+3)^1/2(3x²) (Simplify as much as possible)

What is f'(x)=(15x²+18x)/(2x+3)^1/2?

200

f(x)=(9x²)/(5x+13)

What is f'(x)=(45x²+234x)/(5x+13)²?

300

f(x)=2^xx²

What is f'(x)=x2^x(xln2+2)?

400

f(x)=(2x²)/arctanx

What is f'(x)=2(2)^1/2/arctanx -(2(2)^1/2x)/((1+x²)arctan²x)

500

f(x)=sin²x/(3x³+14x)

What is ((3x³+14x)(2sinxcosx)-(9x²+14)(sin²x))/(3x³+14x)²?

Implicit

100

(d/dx)[4y²+2y+5]

What is 2y'(4y+1)?

200

(d/dx)[3y²+4y+3x+12]

What is 6yy'+4y'+3?

300

(d/dx)[3y²+2yx+2x]

What is 6yy'+2y'x+2y+2?

400

(d/dx)[siny+y²x+2]

What is y'cosy+2yy'+y²?

500

(d/dx)[6cosy/x²]

What is [-6(y'xsiny+2cosy)]/x^3?

Tangent Lines

100

The tangent line using y=4x+3 at x=2

What is y-11=4(x-2)?

200

The tangent line using y=4x²-3x+2 at x=3

What is y-29=21(x-3)?

300

The tangent line when y=ln(x+3) at x=5

What is y-ln8=1/8(x-5)?

400

The tangent line of y=tan(2x)+5 at x=π/8

What is y-6=4(x-π/8)?

500

Tangent line of y=ln(sinx) at x=π/2

What is y=0?

Other

100

This person invented calculus

Who is Isaac Newton or Gottfried Leibniz?

200

True or false: Absolute value is differentiable

What is false?

300

True or False: Continuity implies differentiability.

What is false?

400

Instantaneous rate of change of f(x)=3x³-5x+7 at x=3

What is 76?

500

Average rate of change of f(x)=5x⁵+6x³-2x+5 on [-2,1]

What is 193/3?