A big one!
posted by Jen .
Using logarithmic differentiate technique, find dy/dx
y = [(x3)³(x²+1) / (2x+5)³] raised to the power of 1/5
I don't know how to type this. It is the 5th root of all those.
You have
y = [(x3)³(x²+1) / (2x+5)³]^{1/5}
so
ln y = (1/5)ln([(x3)³(x²+1) / (2x+5)³] =
(1/5){ln([(x3)³(x²+1))  ln(2x+5)³}=
(1/5){3ln(x3) + ln(x²+1)  3ln(2x+5)}
Now find dy/dx and exponentiate your result to get the final result.
I hope I read your superscripts right, they're a little small for me.
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