Find (i) fx (x) (ii) fy V) (iii) are X & Y indepdent? (iv) f, (x/y) (v) (y/x).

Q: Find all the points of g(x, y) = x³ − 3x + 3xy² where a relative extrema might occur.

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Q: Find DF of fcxiy)=x²e° at the point (-2,0)-

A: Given function is fx,y=x2ey. We have to find the ∇f at the point -2,0. We know that ∇f=∂f∂xi+∂f∂yj…

Q: find the orthogonal trajectories of the family of curves x2+y2=a2

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Q: 2 √2x-x² SJ J² J²^ √√√x² + y² + 2 00 y²)[2x − (x² + y²)]dydx -

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Q: 2²y. 3. Consider the function f(, y) =

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Q: Find f, fy. f- f(x.y.z) = 3x - 4y 2. 2 +z?

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Q: Find d²y if y =x² +3x-7 and x=2t+1. dt?

A: y=x2+3x-7 and x=2t+1

Q: Y Is the midpolnt of XZ.If XZ 8x-4 and YZ = 3x +1, find x.

A: Given Y is the mid-point of line segment XZ XZ = 8x-4 YZ = 3x+1   to solve the given question use…

Q: y = x – 2 + Ce* X-

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Q: Find ax dy x-2–1 given y = 2x3

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Q: Find the orthogonal trajectories of the curve x^(2) + y^(2) = c^(2)

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Q: What is the counterexample of x+x>x ?

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Q: find the general equation of : x^3dy+xydx=x^2dy+2ydx  ;y=e when x=2

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Q: Find the relative maxima and minima of y by the second-derivative test: (a) y = -2x2 + 8x = 25…

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Q: Find fx, fy, fz f(x,y,z) = x – V2y² +z?

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Q: Find fxy when f(x, y) = 8xeXy.

A: To find fxy when fx, y=8xexy.

Q: B1. Verify fy = fx for the function f(x,y) = ln(2x- 3y). %3D xy

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Q: Find the ditterential of the function y = (x + 1(5x - 3). Sx-x-5 dy = (Sx - 3) *?+ 6x-5 (5x- 3)? dy…

A: Use the quotient rule of differentiation ddxuv=vdudx-udvdxv2. Power rule of differentiation…

Q: A) Find and classify the critical points of f(z, y) = x³ + y3 – 6y? – 3.x + 9 using the first and…

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: Find the linear approximation to f(x) = at a = 4.

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Q: f(x,y) = (x³ − x)(x² − 1). find fxy(x, ×

A: We have given that ,  fx , y = x3 - x y2 - 1 We need to find , Partial derivative fxy . We know that…

Q: (b) Differentiate (Vx+ 1) with respect to x. 2/3

A: as per our guideline we can solve maximum one question you can repost other questions

Q: Find yll of x³+y²=3 by implicit ditferetlal C1o pants

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Q: Find f2, fy, and f.- f(x, Y, z) = (4x² + 6y² + 3z²)¯05 fz = fy = f. =

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Q: Find a linear approximation of the function f(x) = V1-x at a = 0. %3D

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Q: 2 The Range (Ry) of y = v9 – x² -

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Q: I Sdve for dy using the four-step rule 2. y = x"- x 5X-3 ソ= 4- 3X

A: We have to solve the problem

Q: Let_y=x² +5x³-4x+1 then dy- ||

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Q: What is the value of x in (2x - jy) + (y - jx) = 1 - j5?

A: We have to find the value of x where 2x-jy+y-jx=1-j5

Q: 3 V9-y s S f(1,y)dxdy. y)dzdy. y-3

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Q: Find the linearization of y=2^x at a=0

A: use derivative to find the Linearization of y

Q: What is the counterexample of x/x=1

A: Follow the steps.

Q: Find the orthogonal trajectories of the family of x² – y? = cx = CX -

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Q: Then: f(x, y) = exy 2z3y fxxy 2 2z?y fxxz' XXZ 2z y Ofxyy= x2 Of- 2z3y2 fx² X

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Q: -3x2 F(x) = S*" t² dt %3D

A: TO EVALUATE THE FOLLOWING INTEGRAL F(x) ∫-x3x2 t2 dt FORMULA USED- ∫abxn dx = xn+1n+1 i.e substitue…

Q: which is the best definition of a counterexample

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Q: A particle moves on a vertical line so that its coordinate at time t is y=t3 - 12t + 3 , t>0. When…

A: (b)        y = t3 -12t+3    y1 =3t2 - 12 = v(t) when particle moving up means v(t)>0    3t2…

Q: Calculate fxyy for f(x,y) = x 3 + y2ex.

A: Given function is fx,y=x3+y2ex. To calculate: fxyy. Solution: fxyy means first partial derivative of…

Q: x² – y² = = CX

A: For orthogonal trajectories, replace dy/dx by -dx/dy and solve it.

Q: Find y' for x°y* + 2x + 2y = 128 at the point (2, – 2). At (2, – 2), y' = Preview -

A: The given equation is: x3y4+2x+2y=128...(1) To find y' at the point (2,-2).

Q: Suppose that 3x² - y² = t² and y=tsin 0. Find dy ().-0 (27). and X

A: Given 3x2-y2=t2 and y=tsinθ

Q: Find the orthogonal trajectories of the family of curves x2+y2=a2

A: We have to find the orthogonal trajectories of the family of curves x2+y2=a2.

Q: Show that fy(y) = n[1-Fx(y)]™1 fx(y)

A: Please see that slight information is needed here. which is to be mentioned that    X1, X2,......,…

Q: Find the orthogonal trajectories of the family of curves x3y-xy3=c where c is constant

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Q: What is dufferential equation of x'=4x-y and y'=-4x+4y when t=0, x(0)=1 and y(0)=1

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Q: Find the linearization of the function f(x)=x2+2cosx at a=0.

A: Linearization of a function f(x) at x = a is given by, Now,

Q: Find DF of fcx,y)=x²e° at the point (-2,0)-

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