Common Derivatives Formulas

Basic Properties of Derivatives

\( \left(c \cdot f(x)\right)’ = c \cdot f'(x) \)

\( \left(f \pm g \right)’ = f’ \pm g’ \)

Product rule

\( (f \cdot g)’ = f’ \cdot g + f \cdot g’ \)

Quotient rule

\( \left( \frac{f}{g} \right)’ = \frac{ f’\cdot g – f \cdot g’ }{g^2} \)

Chain rule

\( \left( f \left(g(x) \right) \right)’ = f'(g(x)) \cdot g'(x) \)

Common Derivatives

\( \frac{d}{dx} (C) = 0 \)

\( \frac{d}{dx} (x) = 0 \)

\( \frac{d}{dx} (x^n) = n \cdot x^{n-1} \)

\( \frac{d}{dx} (\sin x) = \cos x \)

\( \frac{d}{dx} (\cos x) = -\sin x \)

\( \frac{d}{dx} (\tan x) = \frac{1}{\cos^2x} \)

\( \frac{d}{dx} ( \sec x) = \sec x \cdot \tan x \)

\( \frac{d}{dx} (\csc x) = – \csc x \cdot \cot x \)

\( \frac{d}{dx} (\cot x) = -\frac{1}{ \sin^2x } \)

\( \frac{d}{dx} (\arcsin x) = \frac{1}{ \sqrt{1-x^2} } \)

\( \frac{d}{dx} (\arccos x) = -\frac{1}{\sqrt{1-x^2}} \)

\( \frac{d}{dx} (\arctan x) = \frac{1}{1+x^2} \)

\( \frac{d}{dx} (a^x) = a^x \cdot \ln a \)

\( \frac{d}{dx} (e^x) = e^x \)

\( \frac{d}{dx} (\ln x) = \frac{1}{x} , x > 0 \)

\( \frac{d}{dx} (\ln |x|) = \frac{1}{x} , x \ne 0 \)

\( \frac{d}{dx} \left( \log_a x \right) = \frac{1}{x\cdot \ln a} , x > 0 \)

Share This Post

Recent Articles

Leave a Reply