Explanation Given information: f ( x , y ) = x y 2 , r ( t ) = 〈 1 2 t 2 , t 3 〉 Calculation: Since ∇ f = 〈 ∂ f ∂ x , ∂ f ∂ y 〉 The given equation f ( x , y ) = x y 2 Differentiating f with respect to x we get, ∂ f ∂ x = ∂ ∂ x x y 2 ⇒ ∂ f ∂ x = y 2 ∂ ∂ x x ⇒ ∂ f ∂ x = y 2 ( 1 ) ⇒ ∂ f ∂ x = y 2 Differentiating f with respect to y we get, ∂ f ∂ y = ∂ ∂ y x y 2 ⇒ ∂ f ∂ y = x ∂ ∂ y y 2 ⇒ ∂ f To determine (b) Toevaluate: d d t f ( r ( t ) ) at t = 1 and t = − 1 .

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

4th Edition

ISBN: 9781319057664

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 14.5, Problem 1E

To determine

(a)

Tocalculate:

∇f and r'(t).

To determine

(b)

Toevaluate:

ddtf(r(t)) at t=1 and t=−1.

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Chapter 14.5, Problem 5PQ

Chapter 14.5, Problem 2E

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Chapter 14 Solutions

CALCULUS EARLY TRANSCENDENTALS W/ACHIEVE

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

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(a) Tocalculate: ∇ f and r ' ( t ) .

Solution Summary: The author explains how to calculate nabla f and r'(t).

Videos

(a)

Tocalculate:

∇f and r'(t).

(b)

Toevaluate:

ddtf(r(t)) at t=1 and t=−1.

Want to see the full answer?

Chapter 14 Solutions

(a) Tocalculate: ∇ f and r ' ( t ) .

Solution Summary: The author explains how to calculate nabla f and r'(t).

Videos

(a) Tocalculate: ∇f and r'(t).

(b) Toevaluate: ddtf(r(t)) at t=1 and t=−1.

Want to see the full answer?

Chapter 14 Solutions

(a)

Tocalculate:

∇f and r'(t).

(b)

Toevaluate:

ddtf(r(t)) at t=1 and t=−1.