Please answer all or do not answer. Thank you :) The Chain Rule and Directional Derivative:...
Answer the two parts. Label each your answers
Find the directional derivative of the function at P in the direction of v. g(x, y) = x2 + y2, P(7, 24), v = 3i - 4j Submit Answer Find the gradient of the function at the given point. Function Point f(x, y) = x + 9y V + 1 (8, 2) 11 1 Vf8, 2) = 1316 Find the maximum value of the directional derivative at the given point.
Exercise 2. Directional derivative (6 pts + 9 pts) Let f(x, y, z) = xy + y2 – 23 – 105. ... touch 25% 17:12 docs.google.com 2) The direction in which f decreases most rapidly at A(0,1,1) is: a. e. None of the above a. b. C. Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy +z-5,x=r+2s,y = 2r - sec(s),z=s
Use the chain rule to find the derivative of 4V50% + 6x8 Type your answer without fractional or negative exponents. Use sqrt(x) for Væ. If f(x) = 7 – x2 5 + x2 find: f'() = Evaluate the limit: 9x – 9 lim 2+1 x2 8x + 7 =
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Calculate the gradient of f(x, y) = sin(x2 – 4y) Vf = Calculate the gradient of h(x, y, z) = x-3y-22-2 Vh= Calculate the directional derivative of S(x,y) = xy in the direction of y = -1 + 2) at the point P = (1,2). Remember to normalize the direction vector. D.$(1.2) = 11 point Calculate the directional derivative of f(x,y) = cos (xy) in the...
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U + tyy = 0. 3. Find the directional derivative of f(x,y) 2In y at the point P(2,1) in the direction ū= 21+ 4. Find the linearization of f(x,y) = x2 + y2 at the point P(3, 4) and use it to
(b) Find the directional derivative of f(x, y, z) = xy ln x – y2 + z2 + 5 at the point (1, -3,2) in the direction of the vector < 1,0,-1>. (Hint: Use the results of partial derivatives from part(a))
In the previous question we used the chain rule to calculate the derivative fog indirectly from the derivatives off and g. Of course, in the previous question f and g were polynomials, and so a simpler method to find the derivative would be to first evaluate f g and then differentiate. However, this "simpler" method does not always work. For example, use the chain rule f(8(x)) = f'(8(x))g'(x) to evaluate: di sin(x3 +1) = d e(x3+1) -1) = datan-1(x3 +...
find the first derivative use chain rule
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7.) y=[sin" (n))" 5.) S(x)=sin(1
Suppose f(x, y) = x2 + y2. Find the directional derivative of the function f at the point P(1, -1) in the direction of 7 = -31 + 4. That is, find Dif(1,-1). 5 14 O 14 5 O 14 5 O 5 14
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or f(x, y, z) x2y + y2 + xz , compute a) the directional derivative at ( 1, 2, 4) in the direction of 12,2,1) , b) the maximum value of the directional derivative of fat (1.2,4), and c) the direction of the minimum directional derivative of fat (1,2,4). (10 pts)
or f(x, y, z) x2y + y2 + xz , compute a) the directional derivative...