Hi

Could someone please show me how to differentiate y = [ln(x)]^(sinx)?

Thanxx a lot!

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- Sep 3rd 2009, 06:06 PMxwrathbringerxImplicit Differentiation Question
Hi

Could someone please show me how to differentiate y = [ln(x)]^(sinx)?

Thanxx a lot! - Sep 3rd 2009, 06:17 PMynj
$\displaystyle (\ln x)^{\sin x}=e^{\ln \ln x\sin x}$

- Sep 4th 2009, 04:06 AMCalculus26
y = ln(x)^(sin(x))

ln(y) = sin(x)ln(ln(x))

1/y dy/dx = cos(x)ln(ln(x) + sin(x) (1/ln(x))1/x

dy/dx = y[cos(x)ln(ln(x) + sin(x) (1/ln(x))1/x]

dy/dx = ln(x)^(sin(x))[cos(x)ln(ln(x) + sin(x) (1/ln(x))1/x] - Sep 4th 2009, 04:22 AMxwrathbringerx
- Sep 4th 2009, 04:31 AMCalculus26
How do you get sin(x)/[xln(x)] simplifying to 1/ln(x) ?

you are not suggesting sin(x)/x =1 are you? - Sep 4th 2009, 04:34 AMHallsofIvy