Calculators / Calculus 1 / Power Rule Calculator

Power Rule Calculator

Published on: April 6, 2025

This Power Rule Calculator helps you differentiate monomials and shows each step clearly. It applies the power rule to expressions of the form a*x^n by multiplying the coefficient by the exponent and then reducing the exponent by 1. This makes it useful for checking answers, understanding how the rule works, and practising calculus step by step.

Step-by-step method

  1. Set up the problem.
  2. Identify the coefficient a and exponent n.
  3. Apply the power rule: d/dx(a·x^n) = a·n·x^(n−1).
  4. Simplify if needed.

Formula:

d
dx
a·xn = a·n·xn−1

Example 1: f(x) = 3x^2

Step 1 - Set up the problem.

In this problem: We will differentiate f(x) with respect to x.

f(x)=3x2

Step 2 - Identify a and n.

In this problem: Match your monomial to a·x^n.

a=3,n=2,x^n=x2

Step 3 - Apply the power rule.

In this problem: Use a·n·x^(n−1).

d
dx
3·x2 = 3·2·x = 6x

Final answer: f'(x) = 6x

Example 2: f(x) = (1/2)x^3

Step 1 - Set up the problem.

In this problem: We will differentiate f(x) with respect to x.

f(x)=
1
2
x3

Step 2 - Identify a and n.

In this problem: Match your monomial to a·x^n.

a=
1
2
,n=3,x^n=x3

Step 3 - Apply the power rule.

In this problem: Use a·n·x^(n−1).

d
dx
1
2
·x3 =
1
2
·3·x2 =
3
2
x2

Final answer: f'(x) = 3x^2/2