Differentiation of function x^x

[Patjamet]

Just wondering if I have done this correctly?

Homework Statement

Differentiate:

$$x^{sin3x}$$

The Attempt at a Solution

$$x^{sin3x}=e^{sin(3x)ln(x)$$

Employing chain rule.

$$y=e^{u}$$
$$u=sin(3x)ln(x)$$

$$dy/dx = e^{u}\times(sin(3x)/x + 3ln(x)cos(3x))$$

Final Solution? =

$$dy/dx = e^{sin(3x)ln(x)}\times(sin(3x)/x + 3ln(x)cos(3x))$$

 

[romsofia]

EDIT: Made a mistake while entering your proposed answer, you're correct.

 

[fzero]

OP is correct. You can compare with http://www.wolframalpha.com/input/?i=d%2Fdx%28x^%28sin%283x%29%29 if necessary.

 

[fzero]

$$x^{sin3x}=e^{sin(3x)ln(x)}$$

The OPs result is equivalent to yours.

 

[Patjamet]

Thanks guys.

May I ask what the "OP" is?

 

[fzero]

Thanks guys.

May I ask what the "OP" is?

Original Post or Original Poster.