Question

Differentiating Exponential functions In Exercise,find the derivative of the function. See Example 2 and 3.

Answer 1

Answer: The derivative of the given function is $f'(x)=\dfrac{2}{x}e^{\frac{1}{x^2}}$

Step-by-step explanation:

Since we have given that

$f(x)=e^{\frac{-1}{x^2}}$

We will derivative it:

So, it becomes,

$f'(x)=-e^{\frac{1}{x^2}}\times (\frac{1}{x^2})'\\\\f'(x)=-e^{\frac{1}{x^2}}\times \dfrac{-2}{x}\\\\f'(x)=\dfrac{2}{x}e^{\frac{1}{x^2}}$

Hence, the derivative of the given function is $f'(x)=\dfrac{2}{x}e^{\frac{1}{x^2}}$