`y = log_3(x^2-3x)` Find the derivative of the function

`y= log_3(x^2-3x)`

The derivative formula of a logarithm is:

`d/(dx) [log_a (u)] = 1/(ln(a) * u) * (du)/(dx)`

Applying this formula, the derivative of the function will be:

`(dy)/(dx) = d/(dx) [log_3 (x^2-3x)]`

`(dy)/(dx) = 1/(ln(3) * (x^2-3x)) * d/(dx) (x^2-3x)`

`(dy)/(dx) = 1/(ln(3) * (x^2-3x)) * (2x - 3)`

`(dy)/(dx) = (2x - 3)/((x^3-3)ln(3))`

Therefore, `(dy)/(dx) = (2x - 3)/((x^3-3)ln(3))` .

Blog