Explanation Given information: f ( x , y , z ) = sin ( x y + z ) , P = ( 0 , − 1 , π ) Calculation: Since the gradient of function is denoted by ∇ f = 〈 ∂ f ∂ x , ∂ f ∂ y , ∂ f ∂ z 〉 The given equation f ( x , y , z ) = sin ( x y + z ) , Differentiating f with respect to x we get, ∂ f ∂ x = ∂ ∂ x sin ( x y + z ) ⇒ ∂ f ∂ x = [ cos ( x y + z ) ] ( ∂ ∂ x ( x y + z ) ) ⇒ ∂ f ∂ x = [ cos ( x y + z ) ] ( y + 0 ) = y cos ( x y + z ) Differentiating f with respect to y we get, ∂ f ∂ y = ∂ ∂ y sin ( x y + z ) ⇒ ∂ f ∂ y = cos ( x y + z ) ∂ ∂ y ( x y + z ) = cos ( x y + z ) ( x + 0 ) = x cos ( x y + z ) Differentiating f with respect to z we get, ∂ f ∂ z = ∂ ∂ z sin ( x y + z ) ⇒ ∂ f ∂ z = cos ( x y + z )<

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Chapter 14.5, Problem 39E

To determine

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Duf(P) where u is a unit vector making an angle θ=30o with ∇fp

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Chapter 14.5, Problem 38E

Chapter 14.5, Problem 40E

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Chapter 14 Solutions

CALCULUS:EARLY TRANS.(LL)-W/ACCESS

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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Tocalculate: D u f ( P ) where u is a unit vector making an angle θ = 30 o with ∇ f p

Solution Summary: The author explains that d_uf(P) is a unit vector making an angle.

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Tocalculate:

Duf(P) where u is a unit vector making an angle θ=30o with ∇fp

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Chapter 14 Solutions

Tocalculate: D u f ( P ) where u is a unit vector making an angle θ = 30 o with ∇ f p

Solution Summary: The author explains that d_uf(P) is a unit vector making an angle.

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Tocalculate: Duf(P) where u is a unit vector making an angle θ=30o with ∇fp

Want to see the full answer?

Chapter 14 Solutions

Tocalculate:

Duf(P) where u is a unit vector making an angle θ=30o with ∇fp