Question

Differentiate Functions of Other Bases In Exercise, find the derivative of the function.

y = log10 (x2 + 6x)

Answer 1

dy/dx = [1/ln(10)][(2x+6)/(x^2 +6x)]

Explanation:

See attachment

Answer 2

`(dy)/(dx) =\frac{2 x + 6}{ \log{\left (10 \right )}\left(x^(2) + 6 x\right)}`

Explanation:

given

`y = log_10((x^2+6x))`

using the property of log
`\log_ab=(log_cb)/(log_ca)`, and if c =
`e`,
`\log_ab=\frac{ln{b}}{ln{a}}`, we can rewrite our function as:

`y = \frac{\ln{\left (x^(2) + 6 x \right )}}{ln(\left (10 \right ))}`

now we can easily differentiate:

`(dy)/(dx) = (1)/(ln(10))\left((d)/(dx)(\ln{(x^(2) + 6x)})\right)`

`(dy)/(dx) = (1)/(ln(10))\left((2x+6)/(x^(2) + 6x)\right)`

`(dy)/(dx) =\frac{2 x + 6}{ \log{\left (10 \right )}\left(x^(2) + 6 x\right)}`

This is our answer!