Question

y = e^(lnx)²

Find the derivative

Answer 1

You need to take the derivative of (lnx)^2 using the product rule and you get 2lnx * the derivative of lnx which is 1/x, so it is (2lnx)(1/x) and you multiply that by the original equation because the base is e. You should end with:\[((2lnx)/x)(e ^{\ln ^{2}x})\]

Answer 2

\[\large {d \over dx} \;\;e^{\ln^2 (x)} =e^{\ln^2 (x)} \cdot {d \over dx}\;\;\ln^2 (x)\]\[\large =e^{\ln^2 (x)} \cdot 2 \ln(x)\; {d \over dx} \;\;\ln(x)=e^{\ln^2 (x)} \cdot {2 \ln(x)\over x}\]

Answer 3

a is real number \[y=a^{f(x)}\]
\[y'=a^{f(x)}*f'(x)*\ln a\]

Answer 4

Thanks guys