Explanation Given: u = u ( t ) , v = v ( t ) , and w = w ( t ) are function of t and kis a constant. Concept Used: The product rule of derivatives: d d x [ f ( x ) ⋅ g ( x ) ] = f ( x ) ⋅ d d x g ( x ) + g ( x ) ⋅ d d x f ( x ) Power rule of derivatives, d d x ( x n ) = n x n − 1 Chain rule, d d x ( f ( g ( x ) ) ) = f ' ( g ( x ) ) ⋅ g ' ( x ) Derivative of any constant C is zero, that is, d d x ( C ) = 0 Derivative of sum of functions: d d x ( f ( x ) + g ( x ) ) = d d x ( f ( x ) ) + d d x ( g ( x ) ) Constant product with derivative: d d x ( c f ( x ) ) = c d d x ( f ( x ) ) , where c is a Calculation: In order to find the derivative d f d t of the given function f ( t ) = 2 v u + w , use product rule, chain rule and power rule of derivative to differentiate implicitly both sides with respect to t as shown below: d f d t = d d t ( 2 v u + w ) = 2 v ⋅ d d t ( u + w ) + u + w ⋅ d d t ( 2 v ) = 2 v ⋅ d d <

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.

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Chapter 3.5, Problem 31S

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Thederivative dfdt of the given function, f(t)=2vu+w .

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Chapter 3.5, Problem 30S

Chapter 3.5, Problem 32S

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Chapter 3 Solutions

Calculus

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Thederivative d f d t of the given function, f ( t ) = 2 v u + w .

Solution Summary: The author explains the product rule of derivatives: dx(c)=0 Derivative of any constant C is zero

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Thederivative dfdt of the given function, f(t)=2vu+w .

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Chapter 3 Solutions