Question

Can I get answers and explanation to this A LEVEL past question a b c d

Answer 1

a.

Given:

The equation is,

`y=(4x^2+5)^2+10\sin 2x`

Step-by-step explanation:

Differentiate the both side of equation with respect to x.

`\begin{gathered} (d)/(dx)y=(d)/(dx)\lbrack(4x^2+5)^2+10\sin 2x\rbrack \\ (dy)/(dx)=(d)/(dx)\lbrack(4x^2+5)^2\rbrack+(d)/(dx)(10\sin 2x) \\ =2(4x^2+5)\cdot(d)/(dx)(4x^2+5)+10\cos 2x\cdot(d)/(dx)(2x) \end{gathered}`
`\begin{gathered} =2(4x^2+5)(8x)+10\cos 2x\cdot2 \\ =16x(4x^2+5)+20\cos 2x \end{gathered}`

So answer is,

`(dy)/(dx)=16x(4x^2+5)+20\cos 2x`