Derivative of a power function

Let $f(x) = x^5$ . Find $f'(x)$ .

Hint

Apply the power rule: $\frac{d}{dx}[x^n] = n x^{n-1}$ , using $n = 5$ .

Step-by-step solution

The power rule states that $\frac{d}{dx}[x^n] = n x^{n-1}$ . Here $n = 5$ , so we bring the exponent 5 down as a multiplying factor and reduce the exponent by 1.

This gives $f'(x) = 5x^{5-1} = 5x^4$ .

Derivative of a power function

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