Question

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

f(x) = e^2x/e^2x + 1

Answer 1

`f'(x)=(2e^(2x))/((e^(2x)+1)^2)`

Explanation:

We are given that a function

`f(x)=(e^(2x))/(e^(2x)+1)`

We have to find the derivative of the function

Differentiate w.r.t x

`f'(x)=(2e^(2x)(e^(2x)+1)-2e^(2x)(e^(2x)))/((e^(2x)+1)^2)`

By using the property

`(d((u)/(v)))/(dx)=(u'v-v'u)/(v^2)`

`(d(e^x))/(dx)=e^x`

`f'(x)=(2e^(4x)+2e^(2x)-2e^(4x))/((e^(2x)+1)^2)`

By using property

`a^x\cdot a^y=a^(x+y)`

`f'(x)=(2e^(2x))/((e^(2x)+1)^2)`