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(4x^{2})

2. y = ln(x^{3}) + (lnx)^{3}

3. y = ln(x^{2} – 5x + 6)

dy/dx = 1/(x^{2} – 5x + 6) * (2x – 5) = (2x – 5)/(x^{2} – 5x + 6)

4. y = ln[(x-1)/x^{2}]^{1/3}