Answer
${dy}=(\frac{5}{2\sqrt{x}}\cos({5\sqrt{x}})){dx}$
Work Step by Step
We evaluate the function: $y=\sin{5\sqrt{x}}$
on differentiating the above:
$\frac{dy}{dx}=\frac{d\sin{5\sqrt{x}}}{dx}$
or $\frac{dy}{dx}=\cos({5\sqrt{x}})\frac{d(5\sqrt{x})}{dx}$
or $\frac{dy}{dx}=\frac{5}{2\sqrt{x}}\cos({5\sqrt{x}})$
or ${dy}=(\frac{5}{2\sqrt{x}}\cos({5\sqrt{x}})){dx}$
The final answer is: ${dy}=(\frac{5}{2\sqrt{x}}\cos({5\sqrt{x}})){dx}$
