anonymous 5 years ago derivative of ln(xe^(7x))

1. anonymous

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

2. anonymous

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

3. anonymous

yeah, sorry, i forgot about product rule :O

4. anonymous

No worries =)