Mr. Integral
Math notes/Calculus I/The Derivative

Power Rules and Linearity — Cheat sheet

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Core rule

Constants differentiate to zero; (af+bg)′=af′+bg′(af+bg)'=af'+bg' for constants a,ba,b.

(xp)′=pxp−1.(x^p)'=px^{p-1}.

Watch for

Check the original domain and differentiability at endpoints or singularities. Linearity does not apply to multiplying two variable functions.