Let y be a function of x and suppose x³+y* - xy =9. What is the correct result for the derivative of y with respect to x? dy 3x2-y A dr 4y dy 3x2-y B dr x- 4y3 dy dr 3x2-y dy 4y3-x

Q: Let f'(a) denote the derivative of the function y = f (x), calculated at x a. Prove that the…

A: Given,                  y= f(x)                      (1)

Q: find the derivative of the function at P0 in thedirection of v. ƒ(x, y, z) = x2 + 2y2 - 3z2, P0(1,…

A: f(x,y,z) = x2 + 2y2 -3z2  v = i + j + k  P0(1, 1, 1)

Q: Consider the implicit relation between x and y defined by ƒ(x) − fƒ(y) + f(xy) = 0 for some…

A: We can solve as follows

Q: Let y be a function of x and suppose *= In(y<-x²). What is the correct result for the derivative of…

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Q: Find the derivative of f(z)= In(z-+-3z+2i). O (A) ƒ'(2) = O (B) ƒ'(2) = O (C) ƒ'(2) =1 – O (D) f'(z)…

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Q: Find the derivative of the function at P in the direction of A g(x, y) = x - (v² /x)+ /3 sec*(2xy),…

A: To find: The derivative of the function at P0=1,1 in the direction of  A=12i+5j Given information:…

Q: Let y be a function of x and suppose *-y*-xy=7, what is the correct result for the derivative of y…

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Q: Find the derivative of the function #1) F(x) = In(2x+3)· (4x +7) tan(x) t +4 dt t2 +2 # 2) h(x)= |

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Q: y = f(x), where f(x) = x4 − 5x. Find the differential of the function. dy = x4−5x

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Q: Let y be a function of x and suppose **- y'- xy =4 What is the correct result for the derivative of…

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Q: 3. If f(r, y) = x*y - 2x-4y, then the total derivative of f

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Q: Evaluate the derivative of the following function at the given point. xy +2x - 5y + 110 = 0; (-3,4)…

A: Differentiate wrt x

Q: Consider the function f(t)=sec^2(t)-3t^3. Let F(t) be the anti derivative of f(t) with F(0)=0. Then…

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Q: Find the derivative of y with respect to x using implicit differentiation in the equation *³y =…

A: We can find the derivative as below.

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 16) y = (x2 - 2x + 1) eX B) (x2…

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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 the derivative of f at point P in the direction of u. f(x, y, z) = 6x² + 2y – 7z?, P = (8,–6,…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the derivative of the function at P0 in the direction of u. f(x, y, z) = -9x + 3y + 8z, P…

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Q: Evaluate the directional derivative of the function f =x² - y° + 2z? at the point A (1,2,3) in the…

A: The directional derivative of a function f at a point a in the direction of a vector v is…

Q: Find the derivative of the function. g(u) = (8+ u²)*(1 – 5u²)8 %3D = (n), 6

A: Now we will differentiate g with respect to  u . And we will  derivative the function using chain…

Q: Find the relation of the derivative of y and y with respect to x, given that yx-y? = 3x 3x II. 1-2xy…

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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 the function at Po in the direction of u. f(x, y) = In( 6 x - 3 y), Po(-7, -4…

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Q: Let y be a function of x and suppose *- y³ – xy = 4, What is the correct result for the derivative…

A: Let y is function of x     x4 - y3 - xy = 4

Q: Which among the following functions has the derivative of dw (18y4 54y³ + 90y²) (2y³ – 1)' + (2y³ –…

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Q: find the partial derivative of the function with respectto each variable. ƒ(R1, R2, R3) = 1/R1+…

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Q: Find the derivative of the function f(z,k) = z^4— 16k^3+ tanh(z) — 4 csc(k) in terms of z and k ?

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Q: Which of the following values is the directional derivative of f (x, y) = 3x² + xy – 2y² – yz + z?…

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Q: Let y be a function of x and suppose x*-y+xy=5_what is the correct result for the derivative of y…

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Q: Let f be a function with continuous second derivatives, defined by: z = f (xy, x² + y") If we take u…

A: Solution:-

Q: find the derivative of the function at P0 in the direction of u. 1.ƒ(x, y, z) = xy + yz + zx, P0(1,…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Let f (z) = (5z +3) (i – xỳhat is the real part of the derivative f' (1+ i}

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Q: Find the derivative of the given function at the point (a, a?, a) in the direction of w = ai + 2aj +…

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Q: Find the derivative of the function. 7x g(x) J6: r7x uZ - 5 du kx u2 + 5 Hint: f(u) du f(u) f(u) du…

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Q: Let y be a function of x and suppose x-y*- xy =7. what is the correct result for the derivative of y…

A: Let's find.

Q: The total derivative of f(x,y )=3 x+ 3 y-41n y is

A: Given function is fx,y=3x3+3y2-4 ln y find the total derivative  dz=fxx,ydx+fyx,ydy

Q: Find the derivative of the function at Po in the direction of A. f(x,y) - - 3ху + 5y, Po(1, - 5), А-…

A: We have to find the directional derivative of the function P at (1,-5).

Q: Find the derivative of the function at Po in the direction of u. x- 5y g(x,y) = Ро(1, - 1), и%3 3і +…

A: To find the derivative of the function  g(x,y)=x-5y5xy+7 at P0(1,-1)in the direction of…

Q: (c) Let f(x.y) = (x²+G))), Determine the directional derivative of f at the point (1,0) in the…

A: f(x,y) = (x2 + (y/2))3 we have to determine the directional derivative of f at the point (1,0) in…

Q: Find the derivative of the function. F(z) = e7/(z – 2) %3D 2e²/(z-2) f'(z) (: – 2)² II

A: f(z)=ezz-2now differentaating both sides with respect to "z"Thenddxf(z)=ddxezz-2…

Q: Suppose x and y are variables (y is a function of x) that satisfy the equation *-y'= 12. What is…

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

A: Solved below.

Q: Let u(x) = C(x) and let v(x) = x. Find the derivative of u(x). O A. u'(x) = C(x)• C'(x) O B. u'(x) =…

A: Answer is Option c is correct  Explanation is given below ..

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: How did he get the derivative? fx (x, y)=-2xe4y–x²-y² fxx (x, y)=-2e4y-r²-y² + 4x²e4y¬x²-y² fy (x,…

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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: Let y be a function of x and suppose y=In(x²+ y²). What is the correct result for the derivative of…

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

A: Find the total derivative

Q: Let y be a function of x and suppose ** – y* – xy =7, What is the correct result for the derivative…

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Q: Let f(x, y) = (x² +(G))°. Determine the directional derivative of f at the point (1 0) in the…

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