Question

First derivative of tan (xsinx)

Answer 1

Start with chain rule:\[\Large\bf\sf \left[\tan(x \sin x)\right]'\quad=\quad \sec^2(x \sin x)\cdot \color{royalblue}{(x \sin x)'}\]Derivative of the outer function tangent, gave us secant squared.
Chain rule tells us to multiply by the derivative of the inner function.
So we have to take the derivative of this blue part.
Make sense so far?

Answer 2

yes yes. Thank you =)

Answer 3

Understand what to do next? :o
Hint hint `product rule`

Answer 4

okay. wait. i'll try..

Answer 5

sec^2 (xsinx) * (xcosx)+(sinx)

Answer 6

Ok very good!
Let's just make sure we put brackets around our product rule to show that the entire thing is multiplying the secant.

sec^2 (xsinx) * [(xcosx)+(sinx)]

Answer 7

Or maybe like this so it's a little easier to read :)

sec^2 (xsinx) * [xcosx+sinx]
But whatev :) Looks like you've got it

Answer 8

aw.. this kills me. my answer was tanx (xcox+sinx) but thanks =))))