Explanation Given: The function, y = e x cos x and the point ( 0 , 1 ) Concept Used: Slope of the tangent line of a function f ( x ) at any point x = c is given by the first derivative at that point. That is the slope of tangent line at x = c is given by f ′ ( c ) . The point-slope form of the line passing through the point ( x 1 , y 1 ) and having slope m is given by y − y 1 = m ( x − x 1 ) . Power rule of derivatives, d d x ( x n ) = n x n − 1 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 ) Derivative of any constant C is zero, that is, d d x ( C ) = 0 d d x ( cos x ) = − sin x d d x ( e x ) = e x Calculation: Consider the function, y = e x cos x In order to find the equation of tangent line, first find the slope of tangent line by finding the first derivative at the specified point

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 3.4, Problem 36E

To determine

The equation of the tangent line to the graph of y=excosx at the point (0,1) .

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Chapter 3.4, Problem 35E

Chapter 3.4, Problem 37E

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Chapter 3 Solutions

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The equation of the tangent line to the graph of y = e x cos x at the point ( 0 , 1 ) .

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The equation of the tangent line to the graph of y=excosx at the point (0,1) .

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