Explanation Given: F ( x ) = tan 2 x and G ( x ) = sec 2 x Formula used: tan x = sin x cos x …………..(1) sec x = 1 cos x …………..(2) d ( u ( x ) v ( x ) ) d x = u ' ( x ) v ( x ) − v ' ( x ) u ( x ) v 2 ( x ) ………(3) cos 2 x + sin 2 x = 1 ………..(4) Calculation: Considering F ( x ) = tan 2 x = sin 2 x cos 2 x ≈ u ( x ) v ( x ) ………( From equation (1) and(2)) F ' ( x ) = ( sin 2 x ) ' ( cos 2 x ) − ( cos 2 x ) ' ( sin 2 x ) cos 4 x …………( From equation (3)) F ' ( x ) = 2 sin x cos x ( cos 2 x ) + 2 sin x cos x ( sin 2 x ) cos 4 x F ' ( x ) = 2 sin x cos x ( cos 2 x + sin 2 x ) cos 4 x F ' ( x ) = 2 sin x cos x ( 1 ) cos 4 x ………………...

4th Edition

ISBN: 9781319434540

Author: Rogawski

Publisher: MAC HIGHER

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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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Question

Chapter 5.3, Problem 68E

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$F (x) = \tan^{2} x$ and $G (x) = \sec^{2} x$ have the same derivative.

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Chapter 5.3, Problem 67E

Chapter 5.3, Problem 69E

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Use the definite integral to find the area between the x-axis and f(x) over the indicated interval. Check first to see if the graph crosses the x-axis in the given interval. 3. f(x) = 4x; [-5,3]

Use the definite integral to find the area between the x-axis and f(x) over the indicated interval. Check first to see if the graph crosses the x-axis in the given interval. f(x)=3e-4; [3,3]

Chapter 5 Solutions

ACHIEVE STANDALONE ACCESS F/ CALC 4E

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F ( x ) = tan 2 x and G ( x ) = sec 2 x have the same derivative.

Solution Summary: The author explains that F (x ) = tan 2 x, and G ( X ), = sec 2x have the same derivative.

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$F (x) = \tan^{2} x$ and $G (x) = \sec^{2} x$ have the same derivative.

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Chapter 5 Solutions

F ( x ) = tan 2 x and G ( x ) = sec 2 x have the same derivative.

Solution Summary: The author explains that F (x ) = tan 2 x, and G ( X ), = sec 2x have the same derivative.

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To show: F(x)=tan2xand G(x)=sec2xhave the same derivative.

Want to see the full answer?

Chapter 5 Solutions

To show:

$F (x) = \tan^{2} x$ and $G (x) = \sec^{2} x$ have the same derivative.