Question

derivative of ln(xe^(7x))

Answer 1

(1/(xe^(7x)))*e^(7x)*7=(7e^(7x))/(xe^(7x))=7/x

Answer 2

That's not actually correct..
\[\frac{d}{dx}ln(xe^{7x}) \]
\[= \frac{1}{xe^{7x}}*\frac{d}{dx}[xe^{7x}]\]
\[= \frac{1}{xe^{7x}}(x\frac{d}{dx}[e^{7x}] + e^{7x}\frac{d}{dx}[x])\]
\[= \frac{1}{xe^{7x}}(xe^{7x}\frac{d}{dx}[7x] + e^{7x})\]
\[= \frac{1}{xe^{7x}}(7xe^{7x} + e^{7x})\]
\[= \frac{7xe^{7x}}{xe^{7x}} + \frac{e^{7x}}{xe^{7x}}\]
\[= 7+ \frac{1}{x}\]

Answer 3

yeah, sorry, i forgot about product rule :O

Answer 4

No worries =)