For the following function {eq}f(x) = 2 e ^{- x ^4} {/eq}.

a) Find {eq}f''(x) {/eq}.

b) Find {eq}f''(0) {/eq}.

c) Find {eq}f'' (1) {/eq}.

Question:

For the following function {eq}f(x) = 2 e ^{- x ^4} {/eq}.

a) Find {eq}f''(x) {/eq}.

b) Find {eq}f''(0) {/eq}.

c) Find {eq}f'' (1) {/eq}.

Finding the Second-Order Derivative:

The expression of the second derivative is {eq}\displaystyle \frac{d{f}'}{dx}={f}''(x) {/eq}. If we differentiate the first-order derivative of the function, we will get the second-order derivative. And it is known as the higher-order derivative. We can evaluate the derivative function at the value of the variable.

Answer and Explanation: 1

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Given function is {eq}\displaystyle f(x) = 2 e ^{- x ^4} {/eq}.

a) Finding {eq}{f}''(x) {/eq}:

{eq}\begin{align*} \displaystyle \text{First...

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Calculating Higher Order Derivatives

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Chapter 8 / Lesson 10
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Higher order derivatives, 2nd, 3rd, and 4th order derivatives, can be calculated using the change in rate of acceleration, known as 'jerk'. Learn how to find these higher order derivatives and the concept of 'jerk' in mathematics.


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