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Derivative of a power function

Let f(x)=x12f(x) = x^{12}. Find f′(x)f'(x).

Hint

Apply the power rule: ddx[xn]=nxn−1\frac{d}{dx}[x^n] = n x^{n-1}. Here n=12n = 12.

Step-by-step solution

The power rule states that for f(x)=xnf(x) = x^n, the derivative is f′(x)=nxn−1f'(x) = n x^{n-1}. Here n=12n = 12, so we bring the exponent down as a coefficient in front of xx.

This gives f′(x)=12x12−1=12x11f'(x) = 12 x^{12-1} = 12x^{11}.

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