Ms. Battaglia AB/BC Calculus. The product of two differentiable functions f and g is itself...
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Transcript of Ms. Battaglia AB/BC Calculus. The product of two differentiable functions f and g is itself...
![Page 1: Ms. Battaglia AB/BC Calculus. The product of two differentiable functions f and g is itself differentiable. Moreover, the derivative of fg is the first.](https://reader036.fdocuments.in/reader036/viewer/2022081603/56649f0e5503460f94c2224f/html5/thumbnails/1.jpg)
2.3 Product & Quotient Rules and Higher-Order Derivatives
Objective: Find the derivative of a function using the Product Rule and the Quotient Rule
Ms. BattagliaAB/BC Calculus
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Theorem 2.7 The Product Rule
The product of two differentiable functions f and g is itself differentiable. Moreover, the derivative of fg is the first function times the derivative of the second, plus the second function times the derivative of the first.
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Using the Product Rule Find the derivative of
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Using the Product Rule Find the derivative of
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Using the Product Rule Find the derivative of
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Theorem 2.8 The Quotient Rule
The quotient f/g of two differentiable functions f and g is itself differentiable at all values of x for which g(x)≠0. Moreover, the derivative of f/g is given by the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator.
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Using the Quotient Rule
Find the derivative of
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Rewriting Before Differentiating
Find the equation of the tangent line to the
graph of at x = -1.
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Original Function
Rewrite Differentiate
Simplify
Using the Constant Multiple Rule
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Derivatives of Trig Functions
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a. y = x – tanx b. y = xsecx
Differentiating Trig Functions
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Different Forms of a Derivative
Differentiate both forms of
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You can obtain an acceleration function by differentiating a velocity function.
Higher-order derivatives: differentiating more than once
Higher-Order Derivatives
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Finding the Acceleration Due to GravityBecause the moon has no atmosphere, a falling object on the moon encounters no air resistance. In 1971, astronaut David Scott proved that a feather and a hammer fall at the same rate of the moon. The position function for each of these falling objects is given by
s(t)=-0.81t2 + 2 where s(t) is the height in meters and t is the time in seconds. What is the ratio of Earth’s gravitational force to the moon’s?
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Read 2.3, Page 126 #19-53 odd, 81, 82, 87, 99, 103, 131-136
Classwork/Homework