Derivatives of Exponential and Logarithmic Functions

Derivatives of  Exponential and Logarithmic Functions

Let’s start with derivatives of the natural log function.

    d/dx(lnu) = 1/u du/dx

    “u” is, as usual, some function of x.

So, if we take the derivative of:        y = ln(x1/2)

We let u =x1/2     then      du/dx =1/2x-1/2

So:    dy/dx = 1/x1/2*1/2x-1/2  = 1/2x

Find dy/dx for each of these.

        1. y = ln(4x2)

        2. y = ln(x3) + (lnx)3

         3. y = ln(x2 – 5x + 6)

            dy/dx = 1/(x2 – 5x + 6) * (2x – 5) = (2x – 5)/(x2 – 5x + 6)

        4. y = ln[(x-1)/x2]1/3