Matt Kwong Blog 4

Hello class! I am Professor Matt and I am going to give you guys a lecture on product and quotient rules for derivatives.

So, when you try to multiply or divide the derivative of a function, we do not do it like normally as we do other math. There are two rules that you need to memorize. They are the product rule and the quotient rule for derivatives.

Now, lets us start with the product rule,

The product rule is: f(x) • g(x) = (f '(x) • g(x)) + (f(x) • g'(x))

It means that the derivative of first function multiply the second function plus the first function multiply the derivative of second function.

Now let us do an example problem.

(3x²)(7x³)

Let f(x) be x and g(x) be (3x²) and g(x) be (7x³).

First we take the product of the derivative of first function and second function.

(6x)(7x³)=42x⁴

Second step, we take the product of first function and the derivative of second function.

(3x²)(21x²)=63x⁴

Finally we add them to get our answer

42x⁴+63x⁴=105x⁴

After the product rule, it is the quotient rule.

(f '(x) • g(x)) - (f(x) • g'(x))

          g²(x)

It is similar to the product rule. You would multiply the derivative of the first function and the second function, and then subtract it by the product of derivative of second function and the first function. After this, divide it by the square of second function.

Let us do an example problem:

x³/(x+4)

Let f(x) be x³ and g(x) be (x+4)

First let find the first part of the top part, multiply the derivative of the first function and the second function

(3x²)(x+4)

Second, we find the second part of the top part, the product of derivative of second function and the first function.

X³(1)=x³

Then we take the square of g(x).

(x+4)²

Finally we put them all together.

[(3x²)(x+4)- x³]/(x+4)²

And we would have the final answer of (2x³+12x²)/(x+4)²

After this lesson, hopefully you all feel confident with the product and quotient rule for derivative.