Answer:
[tex]\dfrac{dy}{dx} =\dfrac{2 x + 6}{ \log{\left (10 \right )}\left(x^{2} + 6 x\right)}[/tex]
Step-by-step explanation:
given
[tex]y = \log_{10}{(x^2+6x)}[/tex]
using the property of log [tex]\log_ab=\frac{log_cb}{log_ca}[/tex], and if c =[tex]e[/tex],[tex]\log_ab=\frac{ln{b}}{ln{a}}[/tex], we can rewrite our function as:
[tex]y = \dfrac{\ln{\left (x^{2} + 6 x \right )}}{\ln{\left (10 \right )}}[/tex]
now we can easily differentiate:
[tex]\dfrac{dy}{dx} = \dfrac{1}{\ln{10}}\left(\dfrac{d}{dx}(\ln{(x^{2} + 6x)})\right)[/tex]
[tex]\dfrac{dy}{dx} = \dfrac{1}{\ln{10}}\left(\dfrac{2x+6}{x^{2} + 6x}\right)[/tex]
[tex]\dfrac{dy}{dx} =\dfrac{2 x + 6}{ \log{\left (10 \right )}\left(x^{2} + 6 x\right)}[/tex]
This is our answer!
Answer:
dy/dx = [1/ln(10)][(2x+6)/(x^2 +6x)]
Step-by-step explanation:
See attachment
