Az Bxm + Cy" – Dx – Ey + 14 where x, y, and z are measured in meter. If you are standing at location (10, 30, 40), by performing second derivatives test, identify A, B, C, D, E, m and n such that (10, 30, 40) is i. local max. ii. local min. ji. saddle points.

Q: The directional derivative of f(z, y,2) = r'y- v': at the point (3,2,1), in the direction of the…

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Q: The derivative of the function y = (10e* – 10x*)(tan x) is: a. y' = (e* – 40x3) tan x + (10e* –…

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Q: What is the derivative of y= 3Arcsin xº, 3 Arcsin x In 3 A y' = 1 - xa 3 Arcsin x* In 3 3 B y' : (а…

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Q: What is the derivative of y = x cos"'(x²)? dy (VI-2²' ) cos' z²+21² dz (VI-zª ) cos' z² –2=² (VI-z4…

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Q: a) Find the directional derivative of a(r, y) = 3-y at (1, 1) in the direction (-3,4). b) Find and…

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Q: S Jiet'. dt Hint: use +he fundam ental theorom Find dy if dx y = of Calculus

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Q: Compute the directional derivative of f(x,y) at the point P in the direction of the point Q. f(x,y)…

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Q: The directional derivative of o = xy²z+ 4x'z at (-1,1,2) in the direction 2i +j- 2k. ans. 38 - 38 3.…

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Q: 3. (D - 3D? + 4)y = 40cos2x + 6

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Q: Find the directional derivative of f(x, y, z) : 4y at P(3,1, –2) x + z in the direction from P to…

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Q: Find the directional derivative of f(x, y) 6x at P(3,0) in the x + Y direction of Q(0,–2). NOTE:…

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Q: Find the directional derivative of f(r,y, z) = e² cos(Tyz) at (0, 1, ) in 2-1 -y-1= I-2 the…

A: To Find: Directional derivative

Q: 4. Write a script which uses finite difference approximations to compute the first derivative dy/dx…

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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 Directional derivative of Hhe function fcauy.)= n (x好) 1- aut point (1,2,1) in the…

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Q: Suppose that f(x, y) the point (x, y) = (2, – 6) is = xy. The directional derivative of f(x, y) in…

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Q: Find the 1st order derivative for    R(x,y) = [(x^2)/(y^2 + 1) ]  -   [(y^2)/(x^2  + y)]

A: Given function is R(x,y)=x2y2+1-y2x2+y Differentiate partially with respect to x.…

Q: Find the derivative of the function f (, y, z) = 4ay z at the point (4, 64, 16) in the direction of…

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Q: Find the directional derivative of f(x, y) at P(5,0) in the %3D x + y direction of Q(3, –3). NOTE:…

A: Given- f(x,y)=20xx+y To find the directional vector of f(x, y) at P(5,0) in the direction of…

Q: The derivative of the function y = xe(5+sec(2x)) is: y' = [1+ 2x sec(2x) tan(2x)]e(5+see(2x)) y' =…

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Q: equation of line normal to f(x) = (x +4)1/2 at Q (0,3) is?

A: Given, f(x)=(x+4)12 To find: Equation of line normal to f(x) at Q(0,3)

Q: 8. Find the directional derivative of f (x, y, z) = xyz3 at P(2, 1, 1) in the direction of Q(0,…

A: Ans=1 I have considered image question bcz I think you have done mistake while typing... Now go…

Q: (3) Consider the derivative dz = 2xydx + (x² + 2y)dy Evaluate whether this is a total derivative, by…

A: We will check whether the given function is total derivative or not. We also integrate dz pathwise.

Q: 2. Determine the directional derivative for u = log, x2lnz if it is defined by the direction at dx =…

A: Given u=logyx2lnzby the direction at dx=dz, dydx=2and is situated at a point in the Euclidean space…

Q: d sec z = sec z tan z dz

A: The function is a rule that associates or fixes a number to the particular point z . If , then the…

Q: In Exercises -. , find the derivative of y with respect to the appro- priate variable. 37. y = sV1 –…

A: Since, you have asked multiple questions we will answer the first one for you. If you want any…

Q: Q4: Find the derivative of the function at P。 in the direction of A 2 1) f(x, y) = 2xy-3y², P (5,5),…

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Q: 8. Find ihe point where the normal to y = x + Vx at (4,6) crosses the y-axis.

A: Given :- Equation of line that is y= x+x              The point from which we need to find the…

Q: 6. Use implicit differentiation to find dy dx x³ + xy-y3 = 7 %3D |

A: Answer: The solution is as given below :

Q: Compute the directional derivative of f(x,y) at the point P in the direction of the point Q. 2…

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Q: What is the value of patrial derivative of z(x,y) with respect to x at x=2, y=4 z=1        none of…

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Q: (c) curve y = 5-x", line y=x+3 (d) y= sinx, y=cosx, x= 7 /4, x=7/2

A: Double integers

Q: If u, v, w are nonzero differentiable functions, then the first derivative of uv / w is

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Q: a*+1 +1 t4 +1 dt with respect to x. Calculate the derivative ol Jsin(x)

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (8, -3)

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Q: 2. Find the directional derivative of f(x, y) = -2e* cos y at %3D (0, ) in the direction of v = (-6,…

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Q: The directional derivative of 2e" cos y at f(x, y) = -2e* cos y at (0, 7) in the direction of v =…

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Q: Evaluate the value of ‘a’ if the first derivative of m(x,y,z)=4-ax^2-2y^2, with respect to the…

A: Consider: mx,y,z=4-ax2-2y2 and mx1,2,3=-2. Solve for a. Calculate mxx,y,z by applying…

Q: 3 ( tann cax) sech' cax) dx Iet v = +anh Cax) = 2 sech cax) dx dx = du 2 sech' cax ) u sech ca* ) du…

A: We  calculate it by using only  calculator. Where we put value of tan(6) as value of tanh(6) and…

Q: Find the derivative of y = Arccot (tan(esecx)) in its simplest form %3D A. y' = e Sec*secxtanx B. y'…

A: This question is related to differentiation, we will solve it using given information.

Q: . The cissoid of Diocles (from about 200 B.C.) Find equations for the tangent line and normal line…

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Q: Find the derivatives of the f: 1. y: sin (x²+3) 6. y= e tan 3x 7. y: e 2. y= tan (4x*) cot (3x-8) 3.…

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Q: 2. Find the directional derivative of f(x, y, z) = y – Væ² + z² at P(-3,1,4) in the direction of a =…

A: Given f(x,y,z)=y-x2+z2

Q: Find the directional derivative of f(x, y, 2) 2y at P(5, 1, –4) a + z in the direction from P to…

A: Given: fx,y,z=2yx+z, P5,1,-4, Q2,3,-1   The expression for the directional derivative of the…

Q: Calculate following derivative if y(t) = 5t-3 + 4t². %3D (Use symbolic notation and fractions where…

A: We have to find

Q: Suppose that f(z, y) = x°y?. Find the directional derivative of f(x, y) in the directional (1, – 1)…

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Q: ху Find all second order derivatives for r(x,y) = 6х + 5y rxx (X,y) = 'yy(x,y) = | ] 'xy (X,y) = ryx…

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Q: Use the figure below to find the unknown value of x * Direction: Given AHND, where AS intersects NH…

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (4, -3)

A: To solve the given line integral.

Q: (D³ + 3D2 + 3D + 2)y = 0

A: Find out the solution.