The Product RuleJordan Hammond

Definition/Steps to SolvingThe Product Rule takes the derivative of a product. It

is used with equations with two or more functions, such as y = f(x)g(x)

So, in order to find the derivative of y = f(x)g(x), you use this formula:

y1 = f(x)g1(x) + f1(x)g(x)

In simpler terms,

y1 = (First term)(Derivative of the Second term) + (Derivative of the First term)(Second term)

F(ds) + dF(s)

Example #1y = (x2)(x + 3x2)

y1 = F(ds) + dF(s)

= (x2)(6x+1) + (2x)(x+3x2)

= 6x3 + x2 + 2x2 + 6x3

= 12x3 + 3x2

y1 = 12x3 + 3x2

Example #2y = (ex)(x3+4)

y1 = F(ds) + dF(s)

(The Derivative of ex is ex)

= (ex)(3x2) + (ex)(x3 + 4)

y1 = (ex)(3x2) + (ex)(x3) + 4ex

Your Turn! Problem #1Find the derivative of the function:

y = (2x)(4x4 + 3x)

Go Again! Problem #2Find the derivative of the function:

y = (3ex)(9x)

Solution to Problem #1y = (2x)(4x4 + 3x)

y1 = F(ds) + dF(s)

= (2x)(16x3+3) + (2)(4x4+3x)

= 32x4+6x+8x4+6x

= 40x4+12x

y1 = 40x4+12x

Solution to Problem #2 y = (3ex)(9x)

y1 = F(ds) + dF(s)

= (3ex)(9) + (3ex)(9x)

= 27ex + 27xex

y1 = 27ex + 27xex