Use radians for trigonometric calculus. Differentiate each term of a sum and retain constant multipliers.

\(\dfrac{\mathrm d}{\mathrm dx}\left(3x^4-2\sqrt{x}+5e^x\right)=12x^3-\dfrac1{\sqrt{x}}+5e^x\), for \(x>0\).

Techniques of Differentiation

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Function	Derivative	Condition
\(x^n\)	\(nx^{n-1}\)	\(n\in\mathbb Q\); where differentiable
\(\sin x\)	\(\cos x\)	Radians
\(\cos x\)	\(-\sin x\)	Radians
\(e^x\)	\(e^x\)	All real inputs
\(\ln x\)	\(\dfrac1x\)	\(x>0\)
\(c\)	\(0\)	Constant

Standard Derivatives