Let y be a function of x and suppose *- y³ – xy = 4, What is the correct result for the derivative of y with respect to x? dy 4x3 – y A dx 3y2+ x dy B Зу2+х y - 4x3 dx dy Зу? +х dx 4x3 – y dy 3y2+x dx y- 4x3

Q: What is the derivative of y = x cos"'(x²)? dy (VI-2²' ) cos' z²+21² dz (VI-zª ) cos' z² –2=² (VI-z4…

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Q: Find the derivative of f : R³ → R² defined by f(x, y, z) = (-3x²y, e-3y-2:). The derivative f' : IR³…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the directional derivative of f(x, y) = 3x² - 2y² at point ,0) to point 3 (-2-1,0) 0(0,1). in…

A: Let's find directional derivative.

Q: Suppose x and y are variables (y is a function of x) that satisfy the equation *2- y³=12, What is…

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Q: find the total derivative of z = f(x,y) = 2x+xy-y2 where x=g(y)=3y2

A: Given function: z=2x+xy-y2 where x=3y2 Putting the value of x in z , we get…

Q: State the theorem for Second Derivative Test for f (x, y).

A: The second-derivative test for maxima, minima, and saddle points has two steps. 1. Find the critical…

Q: Find the derivative of the function at P, in the direction of A 1) f(x, y) = 2xy – 3y², P,(5,5), A=…

A: We have given function, we have to find directional derivative.

Q: Find the derivative of y= (2x³+x+1) 4(x²+3)5 (x4+3) 3 O A dy (4) (2x³+x+1) ³ (5) (x²+3) 4 dx 2(x²+3)…

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Q: he derivative of f(x,y)=10x^y at (e,1) in the direction of v = is

A: From the expression of the directional derivative:   D.D=∇fpx,y,z·a→a→   Given:…

Q: Use the chain rule to find the derivative of f(z) = 4(4z5+5z“) i

A: Given : fx = 44x5+5x4-12

Q: Find the derivative of the function at P, in the direction of A 1) f(x, y) = 2xy – 3y², P,(5,5), A=…

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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: Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional (1, – 1) and…

A: We have to find the directional derivative of the given function in the given direction and at the…

Q: use product rule, find derivative of x.y3 O 1.y3 + x. 3y2y' O 1.y° + x. 3y? O x. 3y2y' noe of the…

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Q: Find the slope of the curve y2 + x² = y* – 2x at (-2,1) Find the required derivative by applying the…

A: topic - slope of curve note - As per bartleby guidelines ,we are supposed to answer only first…

Q: Find the derivative of the function. y=x5 7 3x7 O y'=- 2x3.7 O Y'33 O Y'=. 2x3.7 O Y'=. 3x7 + 5x4…

A: Given, y=x5x3+7

Q: The directional derivative of f(x, y) = ln(xy) + x² at the point (-1,1) in the direction of from the…

A: We have to find the directional derivative.

Q: Find the derivative of the function at the given point in the direction of A. f(x, y) %3DIn(6x -…

A: let an be the unit vector along which we need directional derivative. directional derivative (D.D) =…

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: . Find the directional derivative of y fx, у, 2) x+ z at P(2, 1, – 1) in the direction from P to…

A: NOTE: Refresh your page if you can't see any equations. . the given direction is P to Q find the…

Q: Find the derivative of the function f(x,y,z) = x² + 2y? – 3z2 at the point v =. Po = (1,1,1) in the…

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Q: Suppose x and y are variable (y is a function of x) that satisfy the equation Sin(x+y) =xy, What is…

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Q: 32 Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional (1, 2) and…

A: Given problem:- Suppose that f(x, y) = x3 y2 . The directional derivative of f(x, y) in 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: Suppose that f(x, y) (x, y) (,5) = xy. Find the directional derivative of f(r, y) in the direction…

A: Given

Q: In Exercises -. , find the derivative of y with respect to the appro- priate variable. 37. y = sV1 –…

A: Since, you have asked multiple questions we will answer the first one for you. If you want any…

Q: Suppose that f(x, y) = xy. The directional derivative of f(x, y) in the directional and at the…

A: Explanation of the solution is given below....

Q: Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional and at the…

A: we will find the directional derivative

Q: f(x,y)=ln(5x+4y). Find the directional derivative of f at (1,0) in the direction of the line…

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Q: Suppose that f(x, y) = x*y². The directional derivative of f(x, y) in the directional and at the…

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Q: Suppose that f(x, y) = x°y². The directional derivative of f(x, y) in the directional (- 3, 1) and…

A: First find gradient at point and take dot product with unit vector

Q: The derivative of the function Ve-tanh a is O y = -sech3x vetanh z 2 O y = -sech?x Ve-tanh / 2 O y =…

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

A: Point A(1,2,3) and Point B(5,0,4) ⇒AB→=5-1i^+0-2j^+4-3k^=4i^-2j^+k^ Now we have to find the…

Q: Compute the derivative of f (x, y) = (y + 2) + xysin(x) at (0,1).

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Q: Find the derivative: y = (3x² – 2x) Væ5 – 2x + 2 27 –14a5 –30z² +36x –8 2y5 -2x+2 dy %3D dæ 27+15* –…

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Q: e derivative of y with respect to x. y= 2sin^-1(5x^4

A: we have to find the derivative of y with respect to x.y=2sin-1(5x4)

Q: Use the rules of differentiation to find the derivative of the function y= 3+6sin: a. y' = 3+6cosx…

A: To find the derivative of the below function. y=3+6sinx

Q: If f(x,y) is a real valued function of two variables then what is the second derivative of f?

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Q: Evaluate the required second order partial derivative. Find fxy(5,-1), if f(x,y)= -2xe5y

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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 ƒ(z)= 5z10 – 23 +2 f' (z) = %3D

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

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Q: Suppose that f(z, y) = x°y?. Find the directional derivative of f(x, y) in the directional (1, – 1)…

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Q: Find the derivative of the fünction. y = 7(6 - x2)6 %3D

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Q: Determine the second derivative of 6 y – xy²= I Ay"= 2y³ ( 6 – 2x y)-2 ( 2 - x y ( 6 – 2x y )-1) ®…

A: Let's find.

Q: What is the derivative of y = (sin (3x?)2? dy dr 12z sin' (3교2) VI-974 dy dr 12z sin (3z²) VI-9z4 dy…

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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: Find the partial derivative. Find fx(3, -7) when f(x,y) = 7x2-9xy. O -21 O -126 O 21 O 105

A: differrntiate partially with respect to x

Q: Find the derivative of the function f (x, y, z) = * ++ at the point (-8, 8,-8) in the direction in…

A: Given thta  f(x,y,z)=x/y+y/z+z/x  To find teh derivative of the function at point p in the direction…