Question

differentiate the function w.r.t.x​

Answer 1

Answer:

$\frac{1}{4\sqrt{\sqrt{x}+1}\cdot\sqrt(x)}$

Step-by-step explanation:

$f(x) = (x^{\frac{1}{2}}+1)^{\frac{1}{2}}$

$f'(x) = \frac{(\sqrt{\sqrt{x}+1})^{\frac{1}{2}-1}}{2}\cdot\frac{d(x^{\frac{1}{2}})}{dx}$

$f'(x) = \frac{(\sqrt{\sqrt{x}+1})^{\frac{-1}{2}}}{2}$

$f'(x) = \frac{1}{2\cdot\sqrt{1+\sqrt{x}}} \cdot \frac{1}{2\cdot\sqrt{x}}$

$f'(x) = \frac{1}{4\sqrt{\sqrt{x}+1}\sqrt{x}}$