Question

Math calculus find the first derivative of the given function.

Answer 1

The function is given below as

`\mleft(\sqrt{1-e^(-x)}\mright)\mleft(e^(-x)+1\mright)^2`

By applying the product rule,

`\quad \mleft(f\cdot g\mright)^(\prime)=f\: ^(\prime)\cdot g+f\cdot g`
`(d)/(dx)\mleft(\sqrt{1-e^(-x)}\mright)\mleft(e^(-x)+1\mright)^2+(d)/(dx)\mleft(\mleft(e^(-x)+1\mright)^2\mright)\sqrt{1-e^(-x)}`