CHAPTER 4 MORE

DERIVATIVES

AIM #4.1 HOW DO WE DERIVE COMPOSITE FUNCTIONS? We now know how to differentiate sin x

and x2, but how do we differentiate a composite function, such as sin (x2-4)?

:THE CHAIN RULE

EXAMPLE 1: APPLYING THE CHAIN RULE An object moves along the x –axis so

that its position at any time t>0 is given by

x(t)= cos(t2+1). Find the velocity of the object as a

function of t.

“OUTSIDE-INSIDE” RULE

EXAMPLE 2: Differentiate sin (x2 + x) with respect to

x.

REPEATED USE OF THE CHAIN RULE We sometimes have to use the chain

rule two or more times to find the derivative.

EXAMPLE 3: A THREE-LINK CHAIN Find the dervative of g(t) = tan (5 -

sin2t).

EXAMPLE 3: FINDING SLOPE Find the slope of the line tangent to the

curve y = sin5x at the point where x = . Show that the slope of every line

tangent to the curve y = 1/(1 - 2x)3 is positive.

SUMMARY: ANSWER IN COMPLETE SENTENCES.

When evaluating cos and sin functions on your TI- calculator, what mode should it be in, radian or degree?