Question

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

y = log16(x2 - 3x)

Answer 1

`(dy)/(dx) = (2x-3)/(\ln 16(x^2 - 3x))`

Explanation:

We are given the following in the question:

`y = \ln {16}(x^2 - 3x)`

We have to find the derivative of the given expression.

`y = \ln 16(x^2 - 3x)\\\text{Using the log propert}\\\\\log_a b = (\log b)/(\log a)\\\\frac{d(x^n)}{dx} = nx^(n-1)\\\\(d(\log x))/(dx) = (1)/(x)\\\\\text{\bold{Differentiating we get}}\\\\\displaystyle(dy)/(dx) = (d(\ln 16(x^2-3x)))/(dx)\\\\= (1)/(16(x^2-3x)))(d(x^2-3x))/(dx)\\\\=(1)/(\log 16(x^2-3x))(2x - 3)\\\\= (2x-3)/(\ln 16(x^2 - 3x))`

`(dy)/(dx) = (2x-3)/(\ln 16(x^2 - 3x))`