Derive the formulas for the derivative of a product and the derivative of a quotient from the corresponding formulas for the derivative of a sum and the derivative of a difference.

We know the derivative rules for sums and differences are:

To derive the derivative rule for products using logarithmic differentiation we let and compute

This is the usual rule for derivative of a product.

Similarly, for the derivative of a quotient, let and then compute,

Which is the usual rule for derivative of a quotient.