Question

Find the derivitive of g(x)=lnx^2 Find the derivitive of g(x)=lnx^2 @Calculus1

Answer 1

\[\frac{d}{dx}\ln(x^2)=\frac{1}{x^2}2x=\frac{2}{x}\]

Answer 2

to understand how this was done, you can split the operation into two parts by first letting, say y=x^2 to get:\[g(x)=ln(y)\]so then:\[\frac{dg(x)}{dx}=\frac{dg(x)}{dy}*\frac{dy}{dx}\]now just work out each component of this:\[\frac{dg(x)}{dy}=\frac{1}{y}\]\[\frac{dy}{dx}=2x\]finally:\[\frac{dg(x)}{dx}=\frac{1}{y}*2x=\frac{1}{x^{2}}*2x=\frac{2}{x}\]