Mr. Integral
Math notes/Calculus I/The Derivative

Exponential, Logarithmic and Trigonometric Derivatives — Cheat sheet

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Core rule

(eu)′=u′eu,(ln⁡∣u∣)′=u′/u,(sin⁡u)′=u′cos⁡u,(cos⁡u)′=−u′sin⁡u.(e^u)'=u'e^u,\quad(\ln|u|)'=u'/u,\quad(\sin u)'=u'\cos u,\quad(\cos u)'=-u'\sin u.
(arcsin⁡u)′=u′1−u2,(\arcsin u)'=\frac{u'}{\sqrt{1-u^2}}, (arctan⁡u)′=u′1+u2.(\arctan u)'=\frac{u'}{1+u^2}.

Watch for

Trigonometric formulas use radians. Keep the original function's domain and every inner derivative.