Question

How do you differentiate `y= sqrt(1+x^2)`?

Answer 1

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

Explanation:

Rewrite y as

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

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

`d/dx(f(g(x)))=f'(g(x)).g'(x)....................(A)`
`"--------------------------------------------------------"`

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

`g(x)=1+x^2rArrg'(x)=2x`
`"------------------------------------------------------"`
Substitute these values in (A)

`1/2(1+x^2)^(-1/2).2x=x(1+x^2)^(-1/2)`

`rArrdy/dx=x/(1+x^2)^(1/2)=x/(sqrt(1+x^2)`