Use logarithmic differentiation to find the derivative with respect to x of the function y= (sin x)^lnx
1 answer:
Logarithmic differentiation means tAke logarithm of both sides to make the function easier to find the derivative.
y = (sinx)^lnx
ln(y) = ln((sinx)^lnx)
power rule logarithm
ln(y) = ln(x) ln(sinx)
Take derivative
y'/y = ln(sinx)(1/x) + ln(x) cosx/sinx
multiply both sides by y
y' = y( ln(sinx)/x + ln(x)cotx )
remember y = (sinx)^lnx
sub this in for y
y' = (ln(sinx)/x + ln(x)cotx)(sinx)^lnx
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Answer:
1.85
Step-by-step explanation:
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Hey there!

By using this formula, we plug it in.
Your correct answer would be
. . .
≈

Hope this helps.
~Jurgen
I'm pretty sure its 127.8