Solved: "Derivatives Find and simplify the derivative of the..."

Dillard

Answered question

2021-10-10

Derivatives Find and simplify the derivative of the following functions

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

BleabyinfibiaG

Skilled2021-10-11Added 118 answers

Step 1
The given function is,

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

To find the derivative of the function, we use division rule of derivative,
Step 2

g^{'} (x) = \frac{d}{d x} [f (x)]

= \frac{d}{d x} [\frac{e^{x}}{x^{2} - 1}]

= \frac{(x^{2} - 1) \cdot e^{x} - e^{x} \cdot (2 x - 0)}{{(x^{2} - 1)}^{2}}

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

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

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

Therefore, the derivative of the function is

g^{'} (x) = \frac{e^{x} (x^{2} - 2 x - 1)}{{(x^{2} - 1)}^{2}}

Jeffrey Jordon

Expert2022-08-15Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?