WARM UP: h(x)=f(g(x)). Identify f(x) and g(x). 1. h(x)=sin(2x) 2. h(x)=(x 2 +2) 1\2 3. If h(x)=f(g(j(x))), identify f(x), g(x) and j(x): h(x)=cos 2 (sinx)

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Presentation transcript:

WARM UP: h(x)=f(g(x)). Identify f(x) and g(x). 1. h(x)=sin(2x) 2. h(x)=(x 2 +2) 1\2 3. If h(x)=f(g(j(x))), identify f(x), g(x) and j(x): h(x)=cos 2 (sinx)

Objective: Students will be able to… Use and apply the chain rule of differentiation on composite functions

Suppose you were asked to take the derivative of the following functions. Could you do so with what you know now?

The Chain Rule 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 and Or equivently:

EXAMPLE: Find dy/dx:

Find dy/dx.

Let’s step it up….trickier problems!

I LOVE TRIG!!!!!! 1. y=sin(2x)2. y= tan 2 x

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

Repeated Use of the Chain Rule: y=f(g(h(x))) You may need to apply the chain rule more than once. Take the derivative of the outside function and work your way to the innermost function. 1. f(t) = sin 3 (4t 2 +3t)2. y= 37x –sec 3 (2x)

Find the slope of the tangent line to the curve y=cos 4 t at the point.

Determine the point(s) at which the graph of has a horizontal tangent.

Find the equation of the tangent line at the indicated point. Verify using your calculator.

xf(x)g(x)f’(x)g’(x) Find the value of the derivative of the functions at x=3.