Question

How do you find the derivative of `(1-tanx)^2`?

Answer 1

Derivative of `(1-tanx)^2` is `-2sec^2x+2tanxsec^2x`

Explanation:

We can use Chain rule here. Let `f(x)=(1-tanx)^2`. Then we can write it as

`f(g(x))=(g(x))^2`, where `g(x)=1-tanx`.

Then `(df)/(dx)=(df)/(dg)xx(dg)/(dx)`

= `2xx(1-tanx)xx(-sec^2x)`

= `-2sec^2x+2tanxsec^2x`