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

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Answer 1 · 2016-10-03T09:13:38

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

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 $(df)/(dx)=(df)/(dg)xx(dg)/(dx)$

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

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

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