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

Differentiate y = 4x^3 + 3x + 1.

Back

dy/dx = 12x^2 + 3.

Front

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

Back

f'(x) = -2x.

Front

Differentiate f(x) = x^4.

Back

f'(x) = 4x^3.

Front

Differentiate y = \frac{2x^2 + x - 3}{x}.

Back

y' = 2 + 3x^{-2}.

Front

What is the derivative of a constant?

Back

The derivative of a constant is 0.

Front

Differentiate f(x) = 5x^7.

Back

f'(x) = 35x^6.

Front

Differentiate f(x) = 3x^5 + 2x^3 - x + 4.

Back

f'(x) = 15x^4 + 6x^2 - 1.

Front

What is the derivative of f(x) = x^n when n is a negative integer?

Back

f'(x) = n*x^(n-1), where n < 0.

Front

Differentiate f(x) = 2x^3 - 4x + 7.

Back

f'(x) = 6x^2 - 4.