Question

Derive tan(x)^sin(x)

Answer 1

My closest guess would be something like cosx(tanx)^sinx+sec^2x^sinx, I think...

Answer 2

or \[\cos x(tanx)^{sinx}+\sec ^{2}x ^{sinx}\]

Answer 3

@Callisto hey, sorry to bother you again, but could you help me out on this one?

Answer 4

Do you mean to find the derivative of (i) \((\tan x)^{\sin x}\) or (ii) \(\tan (x^{\sin x})\)?

Answer 5

i) (tanx)^(sinx)

Answer 6

Let's try this:
Let y = (tanx)^(sinx)
ln y = ln [(tanx)^(sinx)]
ln y = (sinx) [ln (tanx)]
Differentiate both sides with respect to x:
\[\frac{1}{y}\frac{dy}{dx} = \sin x \frac{d}{dx}[\ln (\tan x)] + [\ln (\tan x)] \frac{d}{dx}(\sin x)\]Can you do it from here?

Answer 7

yes, i actually just did that after about half an hour of pondering it. thanks again for the help!

Answer 8

Welcome :)