Power Rule Derivatives

Front

What is the Power Rule for derivatives?

Back

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

Front

Find f'(x) when f(x) = 5x^3.

Back

f'(x) = 15x^2.

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) = 2x^5 + 3x^2.

Back

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

Front

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

Back

f'(x) = 4x^3 + 6x^2.

Front

Find the slope of the tangent line to f(x) = x^2 at x = 2.

Back

The slope is 4.

Front

What is the derivative of f(x) = 7x^2 - 4x + 1?

Back

f'(x) = 14x - 4.

Front

Find f'(x) when f(x) = 3x^4 + 2x - 1.

Back

f'(x) = 12x^3 + 2.

Front

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

Back

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

Front

Find the derivative of f(x) = 4x^3 - 2x^2 + 7.

Back

f'(x) = 12x^2 - 4x.