Formulas to calculate derivative -

\frac{d}{dx}(c) = 0 \

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

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

\frac{d}{dx}(e^x) = e^x \

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

Derivative of Trigonometric Functions

\frac{d}{dx}(\sin(x)) = \cos(x) \

\frac{d}{dx}(\cos(x)) = -\sin(x) \

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

\frac{d}{dx}(\cosec(x)) = -\cosec(x) \cot(x) \

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

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

Derivative of Inverse Trigonometric Functions

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

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

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