Explanation Given: The function, y = sin ( cot x ) . Concept Used: The composition function f ∘ g can be found by replacing x by g ( x ) in the function f ( x ) Chain rule, d d x ( f ( g ( x ) ) ) = f ' ( g ( x ) ) ⋅ g ' ( x ) Power rule of derivatives, d d x ( x n ) = n x n − 1 d d x ( cot x ) = − csc 2 x d d x ( sin x ) = cos x Derivative of any constant C is zero, that is, d d x ( C ) = 0 Calculation: In order to express the given function y = sin ( cot x ) as the composition of inner function u = g ( x ) and the outer function y = f ( u ) , observe that the inner function can be taken as u = g

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Chapter 3.5, Problem 4E

To determine

To write thefunction y=sin(cotx) as the composition of inner function u=g(x) and the outer function y=f(u) . And find the derivative dydx .

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Chapter 3.5, Problem 3E

Chapter 3.5, Problem 5E

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To write thefunction y = sin ( cot x ) as the composition of inner function u = g ( x ) and the outer function y = f ( u ) . And find the derivative d y d x .

Solution Summary: The author explains how to write the function y=mathrmsin(MATHRcotx) as the composition of inner and outer functions, and find the derivative

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To write thefunction y=sin(cotx) as the composition of inner function u=g(x) and the outer function y=f(u) . And find the derivative dydx .

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