Logarithmic Differentiation for y=x^{sin(x)}

[crybllrd]

Homework Statement

Find y' using logarithmic differentiation if $$y=x^{sin(x)}$$

Homework Equations

The Attempt at a Solution

$$lny=sin(x)ln(x)$$

$$\frac{1}{y}(y')=sin(x)(\frac{1}{x})+ln(x)\cdot cos(x)$$

$$(y')=[sin(x)(\frac{1}{x})+ln(x)\cdot cos(x)]y$$

Did I do this one properly?
Thanks in advance.

 

[Dick]

It looks fine to me.

 

[jhae2.718]

Looks good to me.

Depending on what the question wants, you may want to sub in $$x^{\sin(x)}$$ for $$y$$ in your final answer. (LaTeX tip: you can use \sin, \cos, and \ln to get "normal" text for sin, cos, ln, etc.)