calculus 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

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

Back

f'(x) = 20x^3.

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) = 7x^3 + 2x.

Back

f'(x) = 21x^2 + 2.

Front

What does the derivative represent in a function?

Back

The derivative represents the rate of change of the function with respect to its variable.

Front

Find the derivative of f(x) = 4x^5 - 3x^2 + 2.

Back

f'(x) = 20x^4 - 6x.

Front

What is the derivative of y = 10?

Back

0, since the derivative of a constant is always zero.

Front

Find the derivative of f(x) = x^2 + 3x + 5.

Back

f'(x) = 2x + 3.

Front

If f(x) = x^n, what is f'(x) when n = 1?

Back

f'(x) = 1.

Front

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

Back

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