Question

What is the derivative of `y= tan(-2x+4)`?

Answer 1

`-2sec^2(-2x+4)`

Explanation:

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

`d/dx(f(g(x)))=f'(g(x)).g'(x)........ (A)`
`"-----------------------------------------"`

`f(g(x))=tan(-2x+4)rArrf'(g(x))=sec^2(-2x+4)`

`g(x)=-2x+4rArrg'(x)=-2`
`"-------------------------------------------"`
Substitute these values into (A)

`rArrdy/dx=sec^2(-2x+4).(-2)=-2sec^2(-2x+4)`