Ms. Battaglia AB/BC Calculus. The chain rule is used to compute the derivative of the composition of two or more functions.

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Presentation transcript:

Ms. Battaglia AB/BC Calculus

The chain rule is used to compute the derivative of the composition of two or more functions.

If 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

y=f(g(x))u=g(x)y=f(u) u=x+1 y=sin2x

Find all points on the graph of for which f’(x)=0 and those for which f’(x) does not exist.

a. y=sin2x b. y=cos(x-1) c. y=tan3x

A. y=cos3x B. y=(cos3x) 2 C. y=cos(3x) 2

Change in distance Change 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 = -16t 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.

 Read 2.4, Page 137 #7-20, 45-50, odd,