Calculus Derivatives

Basic Derivatives

100

The derivative of y = 3x².

What is  y' = 6x?

200

A basic function whose derivative is 0.

What is a constant function?

300

The derivative of f(x) = 6x³ + x - 2.

What is f'(x) = 18x² + 1?

400

The second derivative of f(x) = 3x² - 2x.

What is f''(x) = 6x?

500

A function whose derivative is 3x² + 10x - 5

What is x³ + 5x² - 5x?

Product and Quotient Rule

100

The (simplified) derivative of y = (x²+1)(2x+5).

What is 6x²+10x+2?

200

The simplified derivative of f(x) = (3x - 2x²)(5 + 4x)

What is -24x² + 4x + 15?

300

The derivative of y = (5x - 2)/(x² + 1)

What is (-5x² + 4x + 5)/(x² + 1)²?

400

The derivative of y = ln(x)tan(x)

What is ln(x)sec²(x) + tan(x)/x?

500

Find the derivative of f(x) = (2x + 5)/(x)^1/2

(2x - 5)/(2x^3/2)

Chain Rule

100

Find y' if y = (3x - 9)⁴

12(3x - 9)³

200

f(x) = (2x-1)³ Find f'(x)

6(2x-1)²

300

Find y' if y = (9x² + 4)^1/3

(6x)/(9x² + 4)^2/3

400

Find the derivative of f(x) = (2x-1)^1/2

1/(2x-1)^1/2

500

dy/dx if y=f(u) and u=g(x).

What is dy/du*du/dx?

Exponential and Logarithmic

100

The nontrivial function which is its own derivative

What is the exponential function e^x?

200

The derivative of f(x) = ln(x)

What is 1/x?

300

The derivative of ln(4x³)

What is 3/x?

400

The derivative of f(x) = e^-4x

What is -4e^-4x?

500

The derivative of y = 2^x.

What is y' = ln(2)2^x?

Trig functions

100

The derivative of y = cosh(x)

What is sinh(x)?

200

The derivative of f(x) = sec(x).

What is f'(x) = sec(x)tan(x)?

300

The slope of the line tangent to y = sin(x) at x = pi/6.

What is sqrt(3)/2?

400

The derivative of sin⁵(3x).

What is 15sin⁴(x)cos(x)?

500

The function whose derivative is 1/(1+x²).

What is tan^-1(x)?