Power rule with a large exponent

Let $f(x) = x^{100}$ . Find $f'(x)$ .

Hint

Apply the power rule $\frac{d}{dx}[x^n] = n x^{n-1}$ with $n = 100$ : bring the exponent down as a multiplying coefficient, then subtract 1 from the exponent.

Step-by-step solution

The power rule states that for $f(x) = x^n$ , the derivative is $f'(x) = n x^{n-1}$ . Here $n = 100$ , so we multiply by 100 and reduce the exponent by 1.

This gives $f'(x) = 100 x^{100-1} = 100x^{99}$ .

Power rule with a large exponent

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