# How do you differentiate # f(x)=e^sqrt(1/x^2)# using the chain rule.?

##### 1 Answer

Use

#### Explanation:

**Using the chain rule to differentiate the function as presented:**

# = e^sqrt(1/x^2) * 1/(2sqrt(1/x^2)) d/dx(1/x^2)#

# = e^sqrt(1/x^2) * 1/(2sqrt(1/x^2)) ((-2)/x^3)#

# = (-sqrt(x^2) * e^sqrt(1/x^2))/x^3#

**Rewriting the function as a piecewise function first**

Since

Differentiating each part gets us:

This is equivalent to the answer given above.