power rule
The shortcut \dfrac{d}{dx}[x^n] = nx^{n-1} for differentiating a power of x.
For any real exponent n, \dfrac{d}{dx}\left[x^n\right] = nx^{n-1} — bring the exponent down as a coefficient, then subtract one from it. Constant multiples and sums of terms differentiate independently alongside it.
Examples
\dfrac{d}{dx}[x^5] = 5x^4; \dfrac{d}{dx}[3x^{-2}] = -6x^{-3}.
See also
Point table
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