a.
Given:
The equation is,
[tex]y=(4x^2+5)^2+10\sin 2x[/tex]
Explanation:
Differentiate the both side of equation with respect to x.
[tex]\begin{gathered} \frac{d}{dx}y=\frac{d}{dx}\lbrack(4x^2+5)^2+10\sin 2x\rbrack \\ \frac{dy}{dx}=\frac{d}{dx}\lbrack(4x^2+5)^2\rbrack+\frac{d}{dx}(10\sin 2x) \\ =2(4x^2+5)\cdot\frac{d}{dx}(4x^2+5)+10\cos 2x\cdot\frac{d}{dx}(2x) \end{gathered}[/tex][tex]\begin{gathered} =2(4x^2+5)(8x)+10\cos 2x\cdot2 \\ =16x(4x^2+5)+20\cos 2x \end{gathered}[/tex]
So answer is,
[tex]\frac{dy}{dx}=16x(4x^2+5)+20\cos 2x[/tex]
