1. ## derivative of f(x)=tan^2x^2

Can someone please show me the steps to this problem? Thanks alot

2. ## Re: derivative of f(x)=tan^2x^2

Use the chain rule twice here.

Say $y = \tan ^2x^2$

Find $\frac{dy}{dx}$ where $u = \tan x^2 \implies y = u^2$

what do you get?

3. ## Re: derivative of f(x)=tan^2x^2

Originally Posted by jmanna98
Can someone please show me the steps to this problem? Thanks alot
The derivative of $f^2(x^2)$ is $2[f(x^2)]f'(x^2)(2x).$

4. ## Re: derivative of f(x)=tan^2x^2

f(x)=tan^2x^2
f'(x)=(tanx^2)^2
f'(x)=2(tanx^2)[sec(x^2)(2x)]

Where am I making errors? I am unsure if I am understanding the chain rule properly for trig functions.

My understanding is that you take the derivative of the outside function multiplied by the inside function and multiplied by the derivative of the inside function.

5. ## Re: derivative of f(x)=tan^2x^2

Originally Posted by jmanna98
f'(x)=2(tanx^2)[sec(x^2)(2x)]
That looks correct to me.

6. ## Re: derivative of f(x)=tan^2x^2

You're close. $\frac{d}{dx}\tan(x) = \sec^{2}(x) \ne \sec(x)$

7. ## Re: derivative of f(x)=tan^2x^2

oh...thats what I meant. My bad. Thanks for the confirmation!