Power Rule

Front

What is the Power Rule in calculus?

Back

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

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is always 0.

Front

Differentiate the function f(x) = 5x^3.

Back

f'(x) = 15x^2.

Front

What is the derivative of y = 12x^-2?

Back

y' = -24x^-3.

Front

How do you differentiate a function of the form y = ax^n?

Back

Use the Power Rule: y' = n*ax^(n-1).

Front

What is the derivative of y = 7?

Back

y' = 0.

Front

Differentiate the function y = 4x^2 + 3x + 6x^-2.

Back

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

Front

What is the significance of the exponent in the Power Rule?

Back

The exponent indicates how many times the base x is multiplied by itself, and it is reduced by one when taking the derivative.

Front

If f(x) = x^4, what is f'(x)?

Back

f'(x) = 4x^3.

Front

What is the derivative of y = x^-2?

Back

y' = -2x^-3.