# Thread: logarithmic differentiation

1. ## logarithmic differentiation

Use logarithmic differentiation to find the derivative of f.

f(x)=(3+x)^(2x)

i have 2x ln (3+x)

but i don't know where to go from there...

2. $y=(3+x)^{2x}$

$ln(y)=2xln(3+x)$

$\frac{y'}{y}=\frac{2x}{x+3}+2ln(x+3)$

Now, solve for y and remember what y equals.

3. I got

y'=(3+x)^(2x)*((2x)/(x+3)+2ln(x+3))

4. That's it.