Question

Can someone double-check this derivative for me? In comments, may take a minute to typeset.

Answer 1

\[
\Large f(x)=\sin(x^{\sin(x^{\sin x})})
\]

Answer 2

ick

Answer 3

I'm getting the following result:
\[\Large
f'(x)=\cos(x^{\sin(x^{\sin x})})\cdot x^{\sin(x^{\sin x})}\\\cdot \Large \left[
\cos(x^{\sin x})\cdot x^{\sin x}\cdot \left(\cos x \log x + \frac{\sin x}{x}\right)\cdot \log x +\frac{\sin(x^{\sin x})}{x}
\right]
\]
The answer key in the book has something slightly different, not sure if it's a typo or if I'm confused.

Answer 4

\[\frac{d}{dx}x^{\sin(x)}=x^{\sin(x)}(\cos(x)\ln(x)+\frac{\sin(x)}{x})\] and then the chain rule

Answer 5

Pretty sure it's a typo, it has \((\cos x \log x + \dfrac{\cos x}{x})\), which doesn't make any sense.

Answer 6

no that is not right unless i messed up
gotta run, good luck

Answer 7

My first step was rewriting it as follows:
\[\huge
f(x)=\sin(e^{\sin (e^{\sin x \log x})\log x})
\]

Answer 8

I'm almost positive the answer in the book is wrong, but I just want to double-check before moving on.

Answer 9

you can use wolframalpha to check your steps: http://www.wolframalpha.com/input/?i=d%2Fdx+of+sin%28x^%28sin%28x^%28sin%28x%29%29%29%29%29