What is the derivative of $tan(x^2)$ ?

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Answer 1 · 2016-10-03T00:46:44

$y=tan(x^2)=tan(u)$

$:. (dy)/(du)=sec^2(u)=sec^2(x^2)$

$u=x^2, :. (du)/(dx)=2x$

Use the chain rule...

$(dy)/(du)*(du)/(dx)=2x*sec^2(x^2)=(dy)/(dx)$

Remember that:

If $y=tanx$ , $(dy)/(dx)=sec^2(x)$

It's a general rule.

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