Question

Part 1. Calculus questions ​

Answer 1

Use the chain rule:

`(\mathrm dy)/(\mathrm dx)=(\mathrm dy)/(\mathrm du)\cdot(\mathrm du)/(\mathrm dx)`

With
`y=\cos u`, you have
`(\mathrm dy)/(\mathrm du)=-\sin u`.

With
`u=7x^2`, you have
`(\mathrm du)/(\mathrm dx)=14x`.

So

`(\mathrm dy)/(\mathrm dx)=-14x\sin u=-14x\sin(7x^2)`