Find the derivative of f(x)=e^{5x}+\sin 2x+\cos 3x.


Find the derivative of {eq}f(x)=e^{5x}+\sin 2x+\cos 3x {/eq}.

Differential Calculus:

Differential calculus is used to find the derivative of a function with respect to the independent variable. Derivatives are nothing but the rate of change of the given function.

The formulas used in this problem are:

{eq}\begin{align*} \frac{d}{dx} e^{ax}&=ae^{ax}\\ \frac{d}{dx} \sin ax&=a\cos ax\\ \frac{d}{dx} \cos ax&=-a\sin ax \end{align*} {/eq}

Answer and Explanation:

{eq}\begin{align*} f(x)&=e^{5x}+\sin 2x+\cos 3x\\ f'(x)&=5e^{5x}+2\cos 2x-3\sin 3x&\text{[Differentiate using the formula]} \end{align*} {/eq}

Learn more about this topic:

Differential Calculus: Definition & Applications

from Calculus: Help and Review

Chapter 13 / Lesson 6

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