Question

How do you use the chain rule to differentiate `g(x)=3tan(4x)`?

Answer 1

`g'(x)=12sec^2(4x)`

Explanation:

To differentiate using the `color(blue)"chain rule"`

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

`g(h(x))=3tan(4x)rArrg'(h(x))=3sec^2(4x)`

and `h(x)=4xrArrh'(x)=4`
`color(blue)"-----------------------------------------------------"`
substitute these values into (A)

`rArrg'(x)=3sec^2(4x).4=12sec^2(4x)`