1. ## Derivative

How do I find the derivative of ​$y=sin(tan\,x^2)$

Any help will be appreciated.

2. ## Re: Derivative

just use the chain rule

$\dfrac{dy}{dx} = \cos(\tan(x^2)) \cdot \sec^2(x^2)\cdot 2x = 2x \sec^2(x^2) \cos(\tan(x^2))$

3. ## Re: Derivative

Use chain rule,i.e.,

$\dfrac{d}{dx}f(g(x))=f'(g(x))×g'(x)$

$\Rightarrow \cos(\tan\,x^2) .\dfrac{d}{dx} (\tan\,x^2)$

$\Rightarrow \cos(\tan\,x^2) \sec^2 (x^2) × 2\,x$

Here is the similar question with complete solution

http://www.actucation.com/calculus-1...tric-functions

4. ## Re: Derivative

Originally Posted by Natar
How do I find the derivative of ​$y=sin(tan\,x^2)$

Any help will be appreciated.
$f(x)=\sin(x)$

$g(x)=\tan(x)$

$h(x)=x^2$

$\dfrac{d}{dx}\bigg[f[g(h(x))]\bigg] = \color{red}{f'[g(h(x))]} \cdot \color{blue}{g'(h(x))} \cdot \color{green}{h'(x)}$

$\color{red}{\cos[\tan(x^2)]} \cdot \color{blue}{\sec^2(x^2)} \cdot \color{green}{2x}$

5. ## Re: Derivative

Originally Posted by deesuwalka

$\Rightarrow \cos(\tan\,x^2) \sec^2 (x^2) × 2\,x$
You would not use a "times" sign for multiplication, and especially not separating that quantity for the final form.

At a minimum, you would use a style in post #4 using the multiplication dots, although it is common to place the
"2x" to the far left if someone were to keep simplifying with any additional step(s).