For the function {eq}f(x) = x^{\frac{\displaystyle 6}{\displaystyle 7}} {/eq},

find {eq}f''(x), \; f''(0),\ f''(1), \ {/eq} and {eq}\ f''(-1) {/eq}.

Question:

For the function {eq}f(x) = x^{\frac{\displaystyle 6}{\displaystyle 7}} {/eq},

find {eq}f''(x), \; f''(0),\ f''(1), \ {/eq} and {eq}\ f''(-1) {/eq}.

Second Order Derivative:

The derivative measures the rate of change of a function with respect to a given variable. Different types of functions have different formula for differentiation. If a function {eq}f(x) {/eq} is a differentiable then it will be denoted as {eq}f'(x) {/eq} which is the first derivative. If the function, is differentiable again, then it will be the second derivative {eq}f''(x) {/eq}.

Answer and Explanation: 1

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Given the function, we are asked to find the following. First, find the second order derivative of the function, we have

{eq}\begin{align} f(x) &=...

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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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