Post on 21-Jan-2016
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