Question

cos^-1 x/2 / (2x+7)^1/2,-2

Answer 1

differentiate with respect to x of the function.
$\bf{\frac{cos^{-1}\frac{x}{2}}{\sqrt{2x+7}},-2\leq x\leq2}$

Let $\bf{y=\frac{cos^{-1}\frac{x}{2}}{\sqrt{2x+7}}}$
differentiate with respect to x,
plz see attachment to solve next steps ...

hence, answer is
$\bf{\frac{dy}{dx}=-\left[\begin{array}{c}\frac{1}{\sqrt{4-x^2}\times\sqrt{2x+7}}+\frac{cos^{-1}\frac{x}{2}}{(2x+7)^{3/2}}\end{array}\right]}$