Product Rule


Using the Product Rule


The Product Rule is for finding the derivative of a function that consists of the product of two functions.

If we have two functions multiplied together:

y = u * v

The derivative of this product of two functions is:

dy/dx = u * dv/dx + v * du/dx

Like this: y = x3 (x5 + 3)

Let u = x3 and v = x5 + 3.

Then:     dy/dx = x3 * (5x4) + (x5 +3) * 3x2


dy/dx = 5x7 + 3x7 + 9x2

dy/dx = 8x7 +9x2

(Of course, an easier way to solve this is to multiply it out before you take the derivative, but we wouldn