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(x^1/2)

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

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

Find dy/dx for each of these.

1. y = ln(4x²)

dy/dx = 1/4x² * 8x = 2/x

2. y = ln(x³) + (lnx)³

3. y = ln(x² – 5x + 6)

4. y = ln[(x-1)/x²]^1/3