Question

How do you find the derivative of `f(x)=sqrt(x+1)`?

Answer 1

`f'(x)=1/(2sqrt(x+1))`

Explanation:

`"differentiate using the "color(blue)"chain rule"`

`"given "f(x)=g(h(x))" then"`

`f'(x)=g'(h(x))xxh'(x)larrcolor(blue)"chain rule"`

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

`rArrf'(x)=1/2(x+1)^(-1/2)xxd/dx(x+1)`

`color(white)(rArrf'(x))=1/(2(x+1)^(1/2))=1/(2sqrt(x+1))`