Derivatives (Power Rule)

Front

What is the Power Rule for derivatives?

Back

The Power Rule states that if f(x) = x^n, then the derivative f'(x) = n*x^(n-1).

Front

Find the derivative of f(x) = 12 - 8x.

Back

f'(x) = -8.

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

Find the derivative of f(x) = 7.

Back

f'(x) = 0.

Front

Differentiate the function h(x) = 3x^(5/3) - 6x^(1/6) + 3x.

Back

h'(x) = 5x^(2/3) - x^(-5/6) + 3.

Front

What is the derivative of f(x) = x^n where n is a positive integer?

Back

f'(x) = n*x^(n-1).

Front

Find the derivative of y = 4x^2 + 3x + 6x^(-2).

Back

y' = 8x + 3 - 12/x^3.

Front

What is the derivative of f(x) = x^3?

Back

f'(x) = 3x^2.

Front

Differentiate f(x) = 5x^4 - 2x + 1.

Back

f'(x) = 20x^3 - 2.

Front

What is the derivative of f(x) = 2x^5 + 3x^2 - 4?

Back

f'(x) = 10x^4 + 6x.