Find domain and range F(x,y)= Vx-1

Q: 0,-T <x<0 tsen x, 0sx < T 9. f(x) =

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Q: What does it mean for a function of two variables, f (x, y),to be differentiable at a point (a, b)?

A: A function differentiable at a point has a derivative that is defined at that point. This is defined…

Q: 2. Find the derivative of the function at PO in the direction of u. f(x,y)=6x-7y, P0(-7,-2), u=4i-3j

A: We have to find derivative

Q: Find y" by implicit differentiation. x² + 5y2 = 5 %3D

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Q: Differentiate the function. y = V 3x2 + 8x + 1 dy dx

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Q: Find the derivatives of the functions in Exercis

A: We have, f(x)=7+x sec x First, we write the above function in power form. fx=7+x sec x1/2

Q: 4xy* :- find f,,f, at point (4,1) for f(x,y) = x’e**Y

A: I have used partial differentiation

Q: Find the direction derivative of f(x, y, z) = x²y -zx -yx at the point (1,-1,1) in the direction…

A: Directional derivative using gradient

Q: Differentiate the function.   y = x + 1/ex

A: Case (I): If we have the given function as y=x+1ex        ⋯⋯1 We know that, from the quotient rule…

Q: Differentiate the function. y=(4x-4)° (3-x)? dy dx

A: Given query is to find the derivative of the expression.

Q: Find the derivative of the function = V(=² – 3)* 6, f(x) at x = 2. %3D f'(2) =

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Q: Let f(x,y) be a differentiable function satisfying the equation = xy. %3D ду af and After the change…

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Q: Differentiate the function. 71 y=(9-x) 0 dy | dx

A: We can solve this as follows:

Q: Find the partial derivative f(x,y) = x7y fx(x,y) = ? fy(x,y) = ?

A: The given function is: f(x,y)=x7y

Q: Find the derivative of the transcendental function. y' = y = 6e* x² +8 6(x²–2x+8)ex (x+8)²

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Q: Differentiate the function. y = 7x dy %3D

A: It is derivative problem.

Q: Find the linearization of the function f(x, y) = /36 – læ² – 2y² at the point (3, -1). L(x, y) = Use…

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Q: Let f(x, y) = V xy. Find the derivative of f. af 1 ду 2

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Q: Find all values of x, xe[0,2n] where f(x) = secx has a horizontal tangent line

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Q: For function f(x, y) = 5- | 2 E find the maximum value of the directional derivative at (3, 2).

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Q: Find the derivative of f (y) = 8 tan (y) V √y 8 8 √Y y4

A: The given function is: fy=8tany-y8-8y4y As we know that; The Sum/Difference rule: f±g'=f'±g' The…

Q: Given f(x,y)=e³x² find the directional derivative at the point (-2,0) in the direction of (2,-3)

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Q: Differentiate the function. y= (5x- 1) (1-x°) dy %3D dx

A: Given that the function is      y = (5x-1)2(1-x3)4

Q: Find the directional derivative of f(x, y) = 4x^3 + 3y^2at the point (2, -1) in the direction of v =…

A: The directional derivative of a function can be obtained by evaluating the dot product between the…

Q: Find the derivative of the function f(x, y) = 2x² – y² at the point M = (1, 1) in the direction…

A: We have to find the derivative of the function fx,y=2x2-y2 at the point M=1,1 in the direction…

Q: Use differentiation rules to find y' = dy/dx.

A: To determine the derivative of the function.

Q: The derivative of f(x,y)=9xY at (e,1) in the direction of v=(4,3) is !!

A: TO FIND THE DERIVATIVE i.e DIRECTIONAL DERIVATIVE IN DIRECTION OF V= (4,3) at (e,1) STEPS 1. FIRST…

Q: Differentiate the function. y = In(eX + xe )

A: In this question first apply the property of log and then differentiate as shown...

Q: f(x,y)=x^2+9y^2 What is the direction in which f changes most rapidly at point (1,2)?

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Q: of of For the function f(x,y) = 4x* - 3y' - 8, find and dx of %3D dx of

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Q: The directional derivative of f=8x²y-2xy²+3z at point P(1,1,2) in the direction 2âg+2ây-âz is

A: First we find the gradient of the function f and then unit vector.

Q: Find the derivative using the definition fex)- = C fcx) fCx) = そり f ex) = KX" f cx) fx) = gx).hcx) 9…

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Q: Differentiate the function y = sin1 a 1 y' = Va-x y': a y' =1/x 1 y' Ta- x2 y' =1/a

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Q: The slope of the secant line of the function y =Vx +x through the points x, = 1 and the point xz = 4…

A: y=x+x

Q: · y = Vx - x, (1, 0)

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Q: X~N(3, var=9), Y=7X-6, find pdf of Y

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Q: Let f (2) = – z). (7z+ 10) (i

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

A: We have to solve

Q: Obtain the MSE of f(x) = ex.

A: MSE = Maclaurin Series Expansion f(x)=ex formula f(x)=∑k=0∞f(k)(0)k!xk

Q: Find f'(x)'f f (x)= arctan (Inx) %3D

A: Using composite function formula.

Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. (x, Y)…

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Q: Use differentiation rules to find y′=dy/dx   y = 3 · cos5 ( x − 4/x2 )

A: We apply the power rule then apply the chain rule

Q: Find the derivative of the function. f(z) 0.6z-0.4z2 - 0.8 f' (z) -

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Q: Use differentiation rules to find y' = dy/dx.

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Q: Find the maximum rate of change of the function f(x, y) 4y5 at the point (5,4)

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Q: -2 In(x) Consider the function f(x, y) = 3y

A: We have to find the derivative of the function f(x,y) in the direction u=-5,2.…

Q: Differentiate the function. y=[(sx +2x+3) (x-3)]² dy dx II

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Q: Find the direction at which the function f (x, у, 2) %3 хIn(е' — хг) increases fastest at (-3,0,0)

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Q: What is the maximum value of the directional derivative of f(x, t) = f (x, t) = x² + t²/8 – 10 at…

A: Note: The directional derivative of a function is the rate at which the function changes at a…

Q: find the degree of Precition @F(x)= X

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