Question

Differentiate of the square root of x plus sqaure root of x plus square root of x

Answer 1

`f(x)=\sqrt{x+√(x+\sqrt x)}\\ f(x)=\sqrt{x+\sqrt{x+x^{(1)/(2)}}}\\ f(x)=\sqrt{x+\sqrt{x^{(3)/(2)}}}\\ f(x)=\sqrt{x+\left(x^{(3)/(2)}\right)^{(1)/(2)}}}\\ f(x)=\sqrt{x+x^{(3)/(4)}}}\\ f(x)=\left(x^{(7)/(4)}}\right)^{(1)/(2)}\\ f(x)=x^{(7)/(8)}}\\\\ f'(x)=(7)/(8)x^{-(1)/(8)}`