Question

What is the derivative of `y=tan^2(2x)`?

Answer 1

`4tan2xsec^2 2x`

Explanation:

Differentiate using the `color(blue)"chain rule combined with power rule"`

`color(orange)"Reminder - Chain rule"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(d/dx(f(g(x)))=f'(g(x))g'(x))color(white)(a/a)|))) ........ (A)`
`"----------------------------------------------------------"`

`f(g(x))=tan^2 2x=(tan2x)^2rArrf'(g(x))=2tan2x`

`g(x)=tan2xrArrg'(x)=sec^2 2x.d/dx(2x)=2sec^2 2x`
`"-----------------------------------------------------------"`
Substitute these values into (A)

`rArr2tan2x.2sec^2 2x`

`rArrdy/dx=4tan2xsec^2 2x`