Question

what is the derivative of 6^(lnx^2)

Answer 1

\[\ln x^2 = 2lnx\]

Answer 2

so, yours y = 36^lnx. take ln both sides lny = ln 36^lnx = lnx * ln 36

Answer 3

take derivative is much more easier than original one. hope that helps

Answer 4

If you meant to say
\[y=6^{(\ln x)^2},\]
\[\ln y=(\ln x)^2\ln6\\
\frac{1}{y}y'=2\ln6(\ln x)\frac{1}{x}\\
y'=\ln36\frac{\ln x}{x}\cdot y\\
y'=\ln36\frac{\ln x}{x}\cdot 6^{(\ln x)^2}\]