af Suppose f = f(x, y) and let |(0,5)= 2 and |(0,5) = 8. 3x Define the function g(t) = f(tº - t, 5t). = Then, g'(1) af = ду

Q: ,2 For function f (x, y) x2+1 Evaluate the gradient at the point (1,2)

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Q: a) f„(x, y) b) f (х, у) уу ух 1 3 Зу'х + 5ху 3y'x .3. f (x, у) 16x*y4 -

A: (a)

Q: The domain of F(x, y) =x*y+ x*+ = 1 D =R²- {(0, -)} A O D=R BO D=R? .C O D=R-{}

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Q: Differentiate the function. f(x) = sin(x) In(4x) f'(x) =

A: ddxu(x)v(x)=v(x)ddx(u(x))+u(x)ddx(v(x)) ddx(sin(x))=cosx ddx(ln(ax))=aax=1x…

Q: Consider the function 8 · + 9. xy f(x, y) In which direction does the function f(x, y) increase most…

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Q: 1) y%= (ans.: max.(1,0.5); min.(-1,-0.5)) 1+ x in (2 3-50,8))

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Q: Find f'(2), where f(t) f'(2) = = u(t) · v(t), u(2) = (1, 2, -1), u'(2) = (9, 1, 6), and v(t) = (t,…

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Q: 1. At the point (1, -1), the function (z,y) has a derivative of b in the direction toward (3, 1) and…

A: Given  that at the point (1,−1), the function f(x,y) has a derivative of 5 in the direction toward…

Q: Let h = fog where ƒ : R² → R and g: R² R² is defined by g(x, y) = (3x²y, x – 2y). Find the…

A: Letandfind the derivative

Q: (0,F) (L.F) (L+ F, 0) (L+F+ LF, 0) 2. The following is the graph of f'(x).

A: From the graph,when 0≤x≤L, f'x=F Therefore, f(x)=∫f'xdx=∫F dx=Fx+cc being an integrating constant…

Q: Determine the two-variable function F(x, y) if Fy (x, y) = y sin(xy) + x given that x-² F(x₁ - ²) =…

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Q: The derivative of a function F (X, Y) at a point P_0 = (1,2) in the direction towards P_1 = (2,3) is…

A: Given That : The derivative of a function F (X, Y) at a point P_0 = (1,2) in the direction towards…

Q: the directional d + 3y2 + 5z² at pa

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Q: Find the directional derivative Du f(p) of the following function f

A: Given

Q: -1 A = 0 2) 0. x)T. F(e,) = ( 2

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Q: The graph of f'(x) is shown below. Give the interval(s) where the graph of f(x) is concave up. y =f…

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Q: 5. Use the graph of ƒ '(x) shown and the fact that f(2) = 14 to find the value of f(12). f’(x) 8 3…

A: Notice that the graph of f'(x) on 2,8 is a upper semi circle with center (5,0) and radius 3.…

Q: Determine if f(x, y) = xe*-y + 100y is increasing or decreasing at (-2,1) if a) we allow x to vary…

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Q: Given f(x) = x^5 + x^3 - 4 , find the derivative of f inverse at the point (-2,1).

A: We are given a function as

Q: 3. If f is the function given by f(x) = -x³ + x² + 3x-2, name the open interval where the graph of f…

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Q: Find the x and y coordinates on the graph of f (x) = x³ - 3x where the tangent is horizontal. (A)…

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Q: f(z)=ze^tz/z^2+1 for this function find the Rez(f(z),i) and Rez(f(z),-i) .

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Q: F(t)= t square-root 9-t^2. (-1,3) Find absolute maximum and minimum values

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Q: Let z be a differentiable function of x and y related by the following equation: x + ² =(√y +…

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Q: Find f '(2), where f(t) = u(t) v(t), ū(2) = (1, 2, -1), u' (2) = (3,0, 4), and v(t) = (t, t², t³).

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Q: Let f(x)=(x+4)^3. What are the gradient and equation of the chord/secant between (2,f(2)) and…

A: Given function fx=x+43 The formula for finding the gradient of the chord that passes through 2…

Q: Differentiate the function. (4t + 1)3 (5t – 1)4 F(t) = In F'(t) =

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Q: F'(x) = (ax3 + b)2 O none of the choices O 1 За ах3 + b 1 1 2a ax3 + b 1 1 - За аx3 + b. o 1 2a (…

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Q: FG) ={(g6)) and 861)=2 Fing F'(2)

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Q: 1 Find the derivative of 24 – 3x² +5 글(21-3교2 + 5)글 (4z3 - 6z) 글 (21-3교2 + 5)굴 This function is not…

A: We can take logarithmic to solve it easily.

Q: F(x,y) = In x+y of the function at the point %3D P( 3,4) ond V= [ = -7+ 2 find the derivative %3D in…

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