Consider the following equation f (x,y) = x²y. Find the derivative of f in the direction of (1, 2) at the point (3, 2) is

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A: The given equation is x = y3/3 + y Differentiate on both side with respect to x d/dx(x) = d/dx (…

Q: Find the directional derivative of the following function at P(1, 0) in the direction that produces…

A: Given  fx,y = -3x2+4y3+2xe32y

Q: find the derivative of the function at P0 in the direction of u. ƒ(x, y) = 2x2 + y2, P0(-1, 1), u =…

A:

Q: Find the derivative of y with respect to Z. y=72?)

A: Given,         y=7z2

Q: In what directions is the derivative of ƒ(x, y) = (x2 - y2 )/ (x2 + y2 ) at P(1, 1) equal to zero?

A: Given, , the unit vector is , here directional derivative is given as,

Q: z = Vx4 + yf, fz (1, 2)

A:

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: Find the derivative of y with respect to x if y = (7x - 14x+ 14) eX. %3D dx

A:

Q: Find the derivative of y with respect to X, t, or 0, as appropriate. Inx y=5

A: Given: y=ln xx5 So, the derivative of y with respect to x is: dydx=ddxln xx5 According to the…

Q: (d) Find the directional derivative of f(x, y) = x²e¬y at (-2,0) in the direction towards the point…

A:

Q: Find the derivative of the function. 2x F(x) = arctan(t) dt Vx F'(x) : %D

A: The given problem is to find the derivative of the given definite integral function. We have to use…

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

A: Given : y = xcos-1x+1-2x

Q: Find the derivative of y with respect to x. y = (6x + 5)* dy dx II

A:

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

A:

Q: Use the Fundamental Theorem of Calculus to find the derivative of y- " cos t dt t12

A: Given that  y=∫-9xcos tt12dt

Q: Find the derivative of the function y=ex+2ex at x=0.

A: Given: y=ex+2ex=3ex we know that ddxkex=kex

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: Find the derivative of y with respect to x, t, or 0, as appropriate. Inx y = x7

A:

Q: Find the derivative of the function at Po in the direction of A. f(x,y) = - 4xy + 3y², Po(4, - 2),…

A:

Q: Use the definition of the derivative to show that the derivative of y = f(x)3 2/ is 1 f'(z) = VI %3D

A: GIVEN f(x) = 2√ x CALCULATE f'(x) = 1/ √ x

Q: Find the derivative of a linear function y=ax+b using the definition of derivative.

A: The derivative of a function f' of function f is defined as f'x=limh→0fx+h-fhh

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. y 2xe X- 2e X O 2xeX O 2xeX +…

A: Finding the derivative

Q: Find the derivative of the function. 1 6 y = 4x +8x dy %3D dx

A:

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: Find the derivative of function.

A: Use the product rule to find the derivative for s. s=t2lntdsdt=ddtt2×lnt+t2×ddtlnt

Q: Use the alternative form of the derivative to find the derivative at x = c, if it exists .

A:

Q: Find the derivative of the function at Po in the direction of u. 3x f(x, y) = tan -1 , P0(-2, 3), u…

A:

Q: Find the derivative of the function y(x) = n² +r". Assume that n is a positive y(x) = | constant.

A: You have asked multiple questions and not mentioned which question answer you need so according to…

Q: Calculate the second derivative of the function y = f (x) defined by the equation x3 + y3 +3xy +…

A: Explanation:

Q: Find the derivative of the function. 1 y = 4/x +3x dy dx |00 %3D

A: Use formulas of derivatives to find dy/dx

Q: Calculate the second derivative of the function y = f (x) defined by the equation x³ + y +3xy + 3y²…

A:

Q: Calculate the derivative of the function y(x) given by the equation x2+2xy+2y2=1 under condition…

A: For y=1 we find x

Q: Calculate the derivative of the following function. y = (3x-4x°+4)24 y%3D dy dx

A: Please see the below explanation:

Q: Find the derivative of the following using the three-step rule Зх-1 1. у3D 2x+5 2. y=Va² +x²

A:

Q: Find the derivative of the function f(x, y)=9x² +6y at the point (6,-3) in the direction of v = 3i –…

A:

Q: Find the derivative of y with respect to x. 1. x² + 4y² = 4ay

A: Given:   To find: Derivative of y w.r.t. x:

Q: Find the given flx), + 2x derivative of function. %3D a+x

A:

Q: Consider the function f(z) = V1+z -1 and find its derivative:

A:

Q: Find the derivative of the function at the given point in the direction of A. 3) f(x, y, z) = -10x+…

A: Here initially we need to find out the partial derivative of the given function to find out the…

Q: Find the second derivative of vx - Jy= 4 when x = 1. 2 1 -1 -2

A:

Q: Find the derivative of f(x, y) = (2x – y°, sin(ry), r²y*)

A: Given f(x,y)=2x-y3,sin(xy),x2y3 differentiate f(x , y) with respect to x we get…

Q: Find the derivative of the function at P, in the direction of A. 2 f(x.y) = 4xy- 4y, Po(6,8), A= –…

A:

Q: Find the derivative.

A: Given,

Q: 3r %3D 5r + 2 – 1 (d) f(x) =

A:

Q: find the derivative of the function at P0 in thedirection of v. ƒ(x, y) = 2x2 + y2, P0(-1, 1), v =…

A: Given: fx,y=2x2+y2  We know that, The direction of v is the unit vector obtained by dividing v by…

Q: Find the derivative of y with respect to x if y = (10x- 20x + 20) ex. %3D dy dx

A: We can make it easier for you

Q: The total derivative of the function f(x, y) =3x'y- xy is

A: Find the total derivative

Q: Find the derivative of f(x, y) = e- x ln(y² + 1) at the point R(4,0) in the direction of w = (2, 1).

A: NOTE: Refresh your page if you can't see any equations. . the given vector is find the unit vector

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

Q: Find the derivative of the function. y = sin ( r2 + 1 )

A: Our Aim is to find the derivative of the function given below:-y=sin (r2+1) -(i)