8 Use the gradient to find the directional derivative of the function at P in the direction of Qf(x, y) = sin(3x)cosy, P(0, 0), Q3O3οπO101√√10Oπ(sin(3x)cosy-cos(3x)siny)O π(cos(3x)cosy - sin(3x)siny)T

Answered: Image /qna-images/answer/8c53161a-8104-4df0-9b11-7f2977c2f3b7.jpg

Answered: Use the gradient to find the…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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Let f: R2R be a differentiable function. (a) At the point (ro, yo) = (1,5), it is known that the equation of the tangent plane to the surface z=f(x, y) is -2x+3y-z = 17. Find the directional derivative of f at the point (1,5) in the direction towards the origin.
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Use the gradient to find the directional derivative of the function at P in the direction of Q f(x, y)=sin(3x)cosy, P(0, 0), 3 √10 T 0), Q[T, 17] 1 √10 O л(sin(3x)cosy — cos(3x)siny) 7(cos(3x)cosy-sin(3x)siny)