Question

How do you differentiate `f(x)=xarctansqrtx`?

Answer 1

`=>arctan(sqrtx) + sqrt(x)/(2(1+x))`

Explanation:

`f(x) = x arctan (sqrtx)`

`f'(x) = (d(x))/(dx) arctan(sqrtx) + x (d(arctan(sqrtx)))/(dx)`

`= arctan(sqrtx) + x(1/(1+(sqrtx)^2))(d(sqrtx))/(dx)`

`= arctan(sqrtx) + x/(1+x)*1/(2sqrtx)`

`= arctan(sqrtx) + sqrt(x)/(2(1+x))`