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Find the second derivative of the given function f(x) = e^{2x} + 2e^x.

Question:

Find the second derivative of the given function {eq}f(x) = e^{2x} + 2e^x. {/eq}

Second-order Derivative:

The order of derivative tells us how many times the function is differentiated. If the order of the function is one, means the function is differentiated only once. For the second-order derivative, the function has to be differentiated twice. Collectively all the derivatives having the order of more than one are known as the higher-order derivatives of the function. The chain rule of differentiation is used to differentiate the composite function i.e. one function inside another function, {eq}(f(g(x))) {/eq}. It can be given with the help of the following formula:

{eq}(f(g(x)))' = f'(g(x) ) \cdot g'(x) {/eq}

Also,

{eq}(e^x)' = e^x {/eq}

Answer and Explanation:

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Calculating Higher Order Derivatives

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Chapter 8 / Lesson 10
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Differentiating functions doesn't have to stop with the first or even second derivative. Learn what a mathematical jerk is as you calculate derivatives of any order in this lesson.


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