Calculus

How to solve

The chain rule differentiates a composition by multiplying the outer derivative (evaluated at the inner function) by the inner derivative. For (ax+b)^n that means bring down n, keep the inside, reduce the power, then multiply by a.

Steps

  1. Recognize the outer power and the inner linear expression g(x) = ax + b.
  2. Apply n(ax+b)^{n−1}, then multiply by g'(x) = a.
  3. Simplify coefficients.

Example

Differentiate (2x + 1)⁵.

  1. Outer derivative: 5(2x + 1)⁴.
  2. Multiply by inner derivative 2: 10(2x + 1)⁴.

Answer: 10(2x+1)^4

How to type answers

  • Enter like 10(2x+1)^4
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