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Let f(x) = \begin{cases} e^\frac{1}{x^2} & if\ x \neq 0\\ 0 & if\ x = 0 \end{cases} . Find f'(0)...

Question:

Let {eq}f(x) = \begin{cases} e^\frac{1}{x^2} & if\ x \neq 0\\ 0 & if\ x = 0 \end{cases} {/eq}. Find f'(0) and f(0).

Derivative of a Function:


The derivative of function {eq}y=f(x) {/eq} which can be represented by {eq}y', \ f'(x) {/eq} or {eq}\frac{dy}{dx}, {/eq} is the slope of the tangent line to the curve at a given point.

We can use chain rule, power rule etc. to determine the derivative of the function.

Answer and Explanation: 1

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We have:

{eq}f(x) = \begin{cases} e^{\frac{1}{x^{2}}} & \texttt{if} \ x \neq 0\\ 0 & \texttt{if} \ x = 0 \end{cases} {/eq}.

As per the...

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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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