How do you differentiate $f (x) = {log}_{3} (x e^{x})$ $f(x)=log_3(xe^x)$ ?

Question

5984 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-04-14T03:58:11

$\frac{1}{ln 3}$ $1/ln3$ ( $\frac{1}{x}$ $1/x$ + 1)

First change the base to natural log, f(x)= ln(x $e^{x}$ $e^x$ ) /ln3.

Now differeentiate f' (x) = $\frac{1}{ln 3}$ $1/ln3$ $\frac{d}{d x}$ $d/dx$ ln(x $e^{x}$ $e^x$ )

= $\frac{1}{ln 3}$ $1/ln3$ $\frac{d}{d x}$ $d/dx$ (lnx + x)

= $\frac{1}{ln 3}$ $1/ln3$ ( $\frac{1}{x}$ $1/x$ +1)

How do you differentiate f(x)=log3(xex)f(x)=log_3(xe^x)?