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Find f"(x).

{eq}f(x) = (x^2 + 7)^8 {/eq}

f"(x) =

Question:

Find f"(x).

{eq}f(x) = (x^2 + 7)^8 {/eq}

f"(x) =

Derivative:

The common meaning of the derivative is the rate of change. More precisely, the derivative of any function f(x) with respect to x

indicates the rate of change of f(x) with respect to x.

Rules for derivative:

If {eq}h(x) {/eq} and {eq}g(x) {/eq} are any two functions then,

1. The Sum/Difference rule of derivative is given by {eq}\left(h(x)\pm g(x)\right)^{\prime}=h^{\prime}(x)\pm g^{\prime}(x) {/eq}.

2. The Product rule of derivative is given by {eq}\left(h(x) g(x)\right)^{\prime}=h^{\prime}(x) g(x)+h(x) g^{\prime}(x) {/eq}.

3. The chain rule of derivative is given by {eq}\frac{dh\left(u\right)}{dx}=\frac{dh}{du} \frac{du}{dx} {/eq}.

4. The quotient rule of derivative is given by {eq}\left(\frac{h(x)}{g(x)}\right)^{\prime}=\frac{h^{\prime}(x)~g(x) - h(x)~g^{\prime}(x)}{g(x)^2} {/eq}.

Answer and Explanation: 1

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The given function is {eq}\displaystyle f(x) = (x^2 + 7)^8 {/eq} and we are interested in its second derivative.

First, we find the first derivative...

See full answer below.


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Derivatives: The Formal Definition

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Chapter 7 / Lesson 5
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The derivative in calculus is the rate of change of a function. In this lesson, explore this definition in greater depth and learn how to write derivatives.


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