Introduction to Power Rule for 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), where n is a real number.

Front

Find the derivative of y = 5x^4.

Back

y' = 20x^3.

Front

What is the derivative of a constant?

Back

The derivative of a constant is 0.

Front

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

Back

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

Front

What is the derivative of f(x) = x^n when n = -1?

Back

f'(x) = -1*x^(-2) = -1/x^2.

Front

Find the derivative of f(x) = 7x^5 - 2x + 4.

Back

f'(x) = 35x^4 - 2.

Front

What is the derivative of f(x) = x^0?

Back

f'(x) = 0, since x^0 = 1, a constant.

Front

Find the derivative of f(x) = 3x^2 - 4x + 1.

Back

f'(x) = 6x - 4.

Front

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

Back

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

Front

Find the derivative of f(x) = 4x^2 + 2x - 5.

Back

f'(x) = 8x + 2.