2 3 product and quot rules NOTES September 09, 2016

f(x) = 2x *3

4x , is the derivative simply 6x2 * 4 ?If

compare this tof(x) = 8x

4f '(x) = 32x3

Warm Up

Here is a geometric way to understand the "product rule"

l(x)

w(x) l(x)w(x)

f(x) = l(x) w(x)

Δw

Δl

l(x) Δw

w(x) Δl

when the Δ's are very

small this is gone !

w(x) Δl+Δf(x) = l(x) Δw

Δx Δx Δx

f ' (x) = l(x) w' (x) + l'(x) w(x)

Basically it reads "the first times the derivative of the

2 3 product and quot rules NOTES September 09, 2016

g(x) = (3x - 5)(2x4 + 7)

2 3 product and quot rules NOTES September 09, 2016

Why don't we just multiply the problem out instead of using some long Why don't we just multiply the problem out instead of using some long Why don't we just multiply the problem out instead of using some long Why don't we just multiply the problem out instead of using some long

rule?rule?rule?rule?Yes , if you can multiply it out, do so.

Quite often you can't or it's more work than it's worth

f(x) = 4x cosx2

Find the equation of the line tangent to the

graph f(x) = (x2 - 2x + 1)(x3 - 1) at x = 0

2 3 product and quot rules NOTES September 09, 2016

Differentiate the following function.

2 3 product and quot rules NOTES September 09, 2016

HI

LO=

LOLO

x2 + 5x

4y =

x2 + 5xy =

2 3 product and quot rules NOTES September 09, 2016