Question

How do you differentiate `f(x)=x/(2^sqrt(x-3))` using the chain rule?

Answer 1

`f'(x)=(2^(sqrt(x-3))-1/2(xln2) 2^(sqrt(x-3)) (x-3)^(-1/2))/(2^(sqrt(x-3)))^2`

Explanation:

`f(x)=x/2^(sqrt(x-3))`

Use quotient rule and chain rule

`f=x,` `g=2^(sqrt(x-3))=2^((x-3)^(1/2))`

`f'=1,` `g'=2^((x-3)^(1/2)) ln 2 *1/2(x-3)^(-1/2)*1`

`f'(x)=(2^(sqrt(x-3))-1/2(xln2) 2^(sqrt(x-3)) (x-3)^(-1/2))/(2^(sqrt(x-3)))^2`