In what direction is the derivative of f(x,y)= xy +y at P(4,9) equal Select the correct choice below and, if necessary, fill in the answer

Q: The derivative of z at z e is equal tol. Select one: O a. False b. True

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Q: is differentiable at r 2. 2. (a) Using the definition of derivative, compute for the slope of the…

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Q: Find the derivative Zs and Zt, where Z= e^x+2y, x=s+t^2, y=t+tans

A: Obtain the derivative Zs as follows.

Q: Q2) Find the derivative of the function at Po in the direction of A. g(x, y) = x – (y/x) + V3 sec…

A: Let us consider the function z=f(x,y)  The derivative of the function at point P in the direction of…

Q: Given u(t) = and v(t) =. Find the derivative of u(t) • v(t) at t = 7. Give your answer correct to…

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Q: Given f(z) = x+ VE Calculate the tangent line at the point (16, 20) y : (2- 16) + 20

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Q: Show that the function f(z) = e* – y?(cos(2xy) + isin(2xy)) is entire and find its derivative

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Q: Find the following directional derivative of the function below at P in the direction of Q where,…

A: Directional derivative calculation

Q: Find the derivative of the function using the definition of derivative. dy = lim dx Ar-0 Ar Ay 1.…

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Q: Find the directional derivative of f(x, y) 12x at P(4,0) in the x + y direction of Q(1,–1). NOTE:…

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Q: Find the derivative of the function at P, in the direction of g(x,y) = x - (v² /x)+ /3 sec*(2xy),…

A: Given that  g(x,y)=x-y^2/x+√3arcsecx(2xy) P(1,1) A=12i+5j To find the directional derivative of g at…

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A: Solve

Q: Q:2 In what direction is the derivative of f(x,y) = xy + y° at P (3, 2) equal to zero?

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Q: + (z), V1– 2z y =1- cos (z) + /1 – 2z

A: Given : y = xcos-1x+1-2x

Q: By using the definition of the derivative, use a clear diagram to argue that d S(t)dt = f(x). %3D dx…

A: We have to prove that ddx∫axftdt=fx This will be prove by Newton's Leibnitz rule in this rule we…

Q: Use the second derivative test to find the local extrema of the function f(x, y) = x+ 2xy – 6x –…

A: Step 1: Find the partial derivativesfx and fy and put both equal to zero and we getcritical points…

Q: In what direction is the derivative of ƒ(x, y) = xy + y2 at P(3, 2) equal to zero?

A: Consider the function and solve.

Q: In what direction is the derivative of ​f(x,y)=xy+y^2 at ​P(5​,4) equal to​ zero?

A: Given,

Q: The directional derivative of f(x, yat the point (a, b)in the positive y direction is fr(a, b) O…

A: Use the correct formula for the directional derivative.

Q: The function f(x, y) has a tangent line at (0, 0) with direction . Which of the following are true?…

A: z = f(x,y) f(x, y,) - z = 0 Tangent at (0, 0) with direction <a, 0, c>

Q: Find the derivative of the function at P, in the direction of A g(x,v) = x - (y² /x)+ V3 sec (2xy),…

A: Given that  g(x,y)=x-y^2/x+√3arcsec(2xy) P(1,1) and A=12i+5j To find the directional derivative of g

Q: In what directions is the derivative of f(x,y) = xy + y at P(4,5) equal to zero?

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Q: Given that f(x) = 5x° + x³ + 2, find the derivative of f- by using dy che formula d.x 1 Check dx…

A: To find: The derivative of inverse of f(x)=5x5+x3+2 by the formula dydx=1dxdy. Calculation: Find the…

Q: Find the derivative of f(x, y) = xe + cos(xy) at the point (2,0) in the direction of v=3i-4j. B) 5 O…

A: Please find the answer in next step

Q: Q2: Find the derivative of f(z,x) = xe* + cos(2zx?) at a point (0,2,1)in the direction of V = i - 3j…

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Q: In what directions is the derivative of f(x,y)= xy + y² at P(6,7) equal to zero? Select the correct…

A: To find- In what directions is the derivative of fx, y = xy + y2 at P6, 7 equal to zero?

Q: Find the derivative of the function f(z,k) = z^4— 16k^3+ tanh(z) — 4 csc(k) in terms of z and k ?

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Q: Which of the following values is the directional derivative of f (x, y) = 3x² + xy – 2y² – yz + z?…

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Q: The equation of the tangent line to f(r) = at z = 1 is y = ar +b and the tangent point is (1, c).

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Q: Find the derivative of the function using the definition of derivative. dy Ay lim dx A-0 Ar 1. y=37…

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Q: Using your answer to the previous question, find an equation of the tangent line of f (x) = Va – I…

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Q: Q2) Find the derivative of the function at Po in the direction of A. g(x, y) = x – (y²/x) + V3 sec-'…

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Q: Given u(t) = and v(t) = . Find the derivative of u(t) • v(t) at t = 6. Give your answer correct to…

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Q: The derivative of ƒ(x, y) at P0(1, 2) in the direction of i + j is 2sqrt(2) and in the direction of…

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Q: Given that f(x) = 9x + x³ + 6, find the derivative of f- by using dy the formula dx 1 Check your…

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Q: In what direction is the derivative of f(x,y) = xy + y at P (3, 2) equal to zero?

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Q: The directional derivative of f(x, y) = e" cos Y at (0, ) in the direction of v = (-6, 8) is

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Q: Find the directional derivative of f at P in the direction of a. f (x, y) = 7 tan-1 ; P(-8,8); а%3…

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Q: find the derivative of the function at P0 in the direction of u. ƒ(x, y) = 2xy - 3y2, P0(5, 5), u =…

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Q: In what directions is the derivative of f(x,y) = xy + y at P(8,5) equal to zero?

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Q: Given the curve y2º = x in the xy-plane, for what value of y, if any, does the derivative of y with…

A: Differentiation w.r.t to x

Q: Use linear approximation, i.e. the tangent line, to approximate V1.4 as follows: Let f(x) : Va. The…

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Q: Find the derivative of the function at Poin the direction of A g(x, y) = x – (y²/x) + V3 sec (2ry),…

A: The solution is given as

Q: Which among the choices has the derivative equal to (z+2)? O y = %3D 5 O y = Oy = %3D Z12 Oy= Z12

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Q: Evaluate the derivative of Z F5.png sin (b V) x² f(x) = acosh %3D cx3 if a = 12.91, b = 3, and c = 6…

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Q: Find the derivative of V=(4/3)πr^2b. Assume that b is a constant. dV/dr

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Q: The directional derivative of f(x, y) = e" cos y at (0, ) in the direction of v = (-6,8) is

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Q: Given u(t) = and v(t) =. Find the derivative of u(t) v(t) at t 8. Give your answer correct to two…

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Q: 3 dK Use the definition of the derivative to find for the function K(z) %3D dz 6z + 1"

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Q: Find the derivative of the function f(x, y) = x²y – 4y3 at the point Po(2, 1) in the direction of v…

A: The given function is:  f(x,y) = x2y - 4y3