1. ## log derivatives

y = log 10 (x^2 + 6x)

I'm confused how to proceed here. Can anyone provide a step by step solution?

2. Originally Posted by Archduke01
y = log 10 (x^2 + 6x)

I'm confused how to proceed here. Can anyone provide a step by step solution?
Since log is of base 10, you can apply the formula $\displaystyle \frac{\,d}{\,dx}\left[\log_a u\right] =\frac{1}{u\ln a}\frac{\,du}{\,dx}$

Can you procede?

3. Originally Posted by Archduke01
y = log 10 (x^2 + 6x)

I'm confused how to proceed here. Can anyone provide a step by step solution?
The log is to that base 10 correct?

I'll assume that you know $\displaystyle \frac{d}{du}ln(u)=\frac{1}{u}$

$\displaystyle log_{10}(x^2+6x)=\frac{ln(x^2+6x)}{ln(10)}$

Since $\displaystyle ln(10)$ is a constant, the derivative is

$\displaystyle \frac{1}{ln(10)}\frac{d}{dx}ln(x^2+6x)$

Use the chain rule to obtain:

$\displaystyle =\frac{2x+6}{ln(10)(x^2+6x)}$

4. NOte that I had to edit my original post from an error. I hope I didn't throw you off.

Since $\displaystyle ln(10)$ is a constant, the derivative is
$\displaystyle \frac{1}{ln(10)}\frac{d}{dx}ln(x^2+6x)$