Asked by Anonymous
Find the derivative:
y=x^(sin(x))
y=x^(sin(x))
Answers
Answered by
Reiny
y = x^sinx
take ln of both sides
ln y = ln (x^sinx)
ln y = (lnx)(sinx)
y' / y = lnx(cosx) + (1/x)sinx
y' = y(lnx(cosx) + (1/x)sinx)
= (x^sinx)(lnx(cosx) + (1/x)sinx)
take ln of both sides
ln y = ln (x^sinx)
ln y = (lnx)(sinx)
y' / y = lnx(cosx) + (1/x)sinx
y' = y(lnx(cosx) + (1/x)sinx)
= (x^sinx)(lnx(cosx) + (1/x)sinx)
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