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 y = 3x^5.

Back

15x^4.

Front

What is the derivative of a constant function?

Back

The derivative of a constant function is 0.

Front

Find the derivative of y = 7x^3 + 2x - 5.

Back

21x^2 + 2.

Front

What is the derivative of y = x^0?

Back

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

Front

Find the derivative of y = 4x^2 - 3x + 7.

Back

8x - 3.

Front

What is the derivative of y = 1/x?

Back

-x^(-2) or -1/x^2.

Front

Find the derivative of y = 2x^4 + 3x^2 - x.

Back

8x^3 + 6x - 1.

Front

What is the derivative of y = e^x?

Back

e^x.

Front

Find the derivative of y = 5x^6.

Back

30x^5.