Super Calc Bros (Derivative Edition)

Power Up!

100

The derivative of x⁴

What is 4x³

200

The derivative of 5x^-2

What is -10x^-3

300

The derivative of x^1/2 + e^x

What is 1/2(x)^(1/2) + e^x

400

The derivative of x³(2x-1)

What is 3x²(2x-1) + x³(2)

500

The derivative of e^3xx²

What is 3e^3x(x²) + 2x(e^3x)

Rule Breakers

100

The derivative of ln(2x)

What is 1/x

200

The derivative of cos(5x)

What is -5sin(5x)

300

The derivative of (3x)/(x+1)

What is 3/(x+1)²

400

The derivative of x²(sinx)

What is 2x(sinx) + x²(cosx)

500

dy/dx given x² + y² = 25 is

What is -x/y

Rate It or Hate It

100

f'(2) given f(x) = x³

What is 12

200

The velocity at t=4 if s(t) = t² - 3t

What is 5

300

The circle's radius increases by 2cm/s, so the rate of change of the area when r=3

What is 12pi

400

f(x) = x³ - 3x is increasing when

What is (-∞, -1) U (1, ∞)

500

A 10ft long ladder leans on a wall and the bottom slides away at 1 ft/s. How fast does the top slides down when the bottom is 6 ft from the wall

What is -0.75 ft/s

Trig or Treat

100

The derivative of sinx

What is cosx

200

The derivative of cos(2x)

What is -2sin(2x)

300

The derivative of tanx

What is sec²x

400

The derivative is arcsin(x)

What is 1/(1-x²)^1/2

500

The derivative of sin(x²)

What is 2xcos(x²)

Integral-ish

100

The integral of x² dx

What is x³/3 + C

200

The integral of 4e^x dx

What is 4e^x + C

300

The integral of 1/x dx

What is ln|x| + C

400

The integral of 6x(x² + 1)² dx

What is (x² + 1)³ + C

500

f(1) = 2, given f'(x) = 3x² - 4 (solve for C and rewrite equation)

What is y = x³ - 4x + 5