Question

Log_{7 }(5 - 3x)
Find the derivative​

Answer 1

Let y be the expression you want to differentiate:

`y=\log_7(5-3x) \implies 7^y=5-3x`

Now,

`7^y=e^(\ln(7^y))=e^(y\ln(7))`

Use the chain rule to differentiate both sides with respect to x :

`\ln(7)e^(y\ln(7))(\mathrm dy)/(\mathrm dx)=-3`

Solve for dy/dx :

`\ln(7)7^y(\mathrm dy)/(\mathrm dx)=-3`

`(\mathrm dy)/(\mathrm dx)=-\frac3{\ln(7)7^y}`

`(\mathrm dy)/(\mathrm dx)=\boxed{-\frac3{\ln(7)(5-3x)}}`