# How to solve this derivative? with steps

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# \frac(1)(e^x + \sqrt {e^x + 1}#

##### 2 Answers

#### Explanation:

Writing your term in the form

the second factor Comes from the chain rule, if we

differentiate

#### Explanation:

Take it in small steps. break the problem down into pieces, and solve those, then put everything together

Start with the formula for finding the derivative of the quotient of 2 functions:

...this problem allows at least some simplification since the numerator is the constant 1, so

So, if we denote the denominator in the original function as g(x), the derivative is:

We have to then find

We know that

...rewrite the square root term as

...you find this using the chain rule, and the rule for finding derivatives of powers of functions:

so

so, going back to

...you can rewrite this as:

and now, all we have to do is find

...and that's just a simple binomial multiplication:

So now, you can put all this together:

GOOD LUCK