Question

How do you differentiate `f(x) = Tan^(-1) (x/2)`?

Answer 1

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

Explanation:

`•color(white)(x)d/dx(tan^-1x)=1/(1+x^2)`

`"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)=tan^-1(x/2)`

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

`color(white)(rArrf'(x))=(1/2)/(1+x^2/4)xx4/4`

`color(white)(rArrf'(x))=2/(4+x^2)`