ms. battaglia ab/bc calculus. the chain rule is used to compute the derivative of the composition of...
TRANSCRIPT
2.4 The Chain RuleObjective: Find the derivative of a composite function
using the Chain Rule
Ms. BattagliaAB/BC Calculus
The Chain RuleThe chain rule is used to compute the derivative of the composition of two or more functions.
Theorem 2.10 The Chain RuleIf y = f(u) is a differentiable function of u and u = g(x) is a differentiable function of x, then y = f(g(x)) is a differentiable function of x then
Differentiating Functions Involving RadicalsFind all points on the graph of for which f’(x)=0 and those for which f’(x) does not exist.
Find the equation of the tangent line to the graph of
at the point (π,1). Then determine all values of x in the interval (0,2π) at which the graph of f has a horizontal tangent.
Tangent Line of a Trig Function
Change in distanceChange in time
Ex: A billiard ball is dropped from a height of 100 ft, its height s at time t is given by the position function s = -16t2 + 100 where s is measured in feet and t is measured in seconds. Find the average veolcity over the time interval [1,2]. Find the instantaneous velocity at t=1.
Average velocity