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