CalcRef

Derivatives · Basic Rules

Power Rule

ddx[xn]=nxn−1\frac{d}{dx}[x^n] = nx^{n-1}

Bring the exponent down as a coefficient and reduce the exponent by one. Works for any real number n.

Conditions. n can be any real number. For n = 0 the result is 0.

Worked examples

Find d/dx[x⁵].
  1. Apply power rule: 5x⁴

Answer: 5x⁴

Find d/dx[x^(-2)].
  1. Apply power rule: -2x^(-3) = -2/x³

Answer: -2/x³

Find d/dx[√x].
  1. Rewrite: √x = x^(1/2)
  2. Apply power rule: (1/2)x^(-1/2) = 1/(2√x)

Answer: 1/(2√x)

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