Use the definition of partial derivative of a function f(x, y) = 3x² – xy? to illustrate fi and f2 '

Q: Find the direction derivative of f(x, y, z) = x²y -zx -yx point (1,-1,1) in the direction 3i+4k x at…

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Q: Find the directional derivative of f(x, y, z) = -4x? + ly? – 4z2 at the point (0, -4, 2) in the…

A: Given function

Q: Find the derivative of f(x, y) = xey + cosxy at the point (2,0) in the ection.

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

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: Consider f(x, y) =(ax² + by²). Based on the second derivative test, what are the conditions…

A: Answer

Q: Calculate the derivative of f (x) = cos (7æ³ + 2) %3D showing all your work.

A: Topic-derrivative

Q: I need help with this question

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Q: Determine the derivative of the function defined by h(x,y) = Arctan (2) + V3Arcsin () at the point…

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Q: A curve y = f(x) have length of the curve from x = 0 to x = 1/2. dy Vcos(2x – 2) as its first…

A: We have to find

Q: Find the linear approximation of the function at the given point. f(x, y) = 4 sinx - 6 cos y at (0,-

A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

Q: Obtain the derivative of the function y 4y sen (3x) – 7x In(2x + y) = e* - ey + 4tg(y)

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Q: What is the derivative of cosh-1(xy) + elog x = sec3(y2)

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Q: Find the derivative of the function. y = ek tan(V 5x) y'(x)

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Q: 2.Evaluate the total derivative of u with respect to x for u = 4x4+3y² + 3z² when y = sinx and z =…

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Q: find the first order derivative of y=sin 0.5√x/x at x=8, h=0.2 a. Forward difference B. Backward…

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Q: Find the derivative of ƒ(x, y) = xey + cos (xy) at the point (2, 0) in the direction of v = 3i - 4j.

A: Given: f(x,y)=xey+cos(xy) at point (2,0) in the diection of v=3i−4j

Q: Find all the critical points of f(2z, v) = - . 1 + 4x – xy? and classify them using the second…

A: The given function is;  f(x)=-x3/3 +4x -xy2.

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: Calculate the partial derivative using implicit differentiation of + = 10 at (x, y, w) = (1,2, 1).…

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

Q: the derivative of y with respect to v. 1 = In ( cosh (5v)) –· tanh 2(5v) 2 derivative of y with…

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Q: 5. Use Implicit differentiation to find dy when y V x2 tya = 15x° +4siny 3

A: Using implicit differentiation find dydx for;  yx2+y2=15x3+4siny

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: Consider f(x) = 3 − cosx on the interval [0, 7]. When will the first derivative equal zero?

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Q: What is the derivative of y = sin1 (x² + 2)? dy dr /1-(z²+2)² dy O dr 2x V1-(2²+2)² O dz V1+(x²+2)²…

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Q: 2x f(x) sec(t*) dt. %3D -2x

A: Given,            f(x) =∫-2x2xsect4 dt

Q: What is the derivative of y = tan-1(x2 + 1)? dy dr 2 1+( z²+1)² dy dr /1+(z²+1)² dy O dr V1+(2+1 )°…

A: To find derivative of y=tan-1x2+1

Q: Compute the indicated derivative using the chain rule. dy x = 1 - t/3, y = 8t – 1;- dx dy dx

A: x=1-t3 differentiating with respective t dxdt=-13 y=8t-1 differentiating with respective t dydt=8

Q: Calculate the partial derivative using implicit differentiation of x'w + w + wz? + 3yz = 0. (Use…

A: Use the following formulas: 1.∂∂xxn=nxn-12.∂∂x(a.b)=a.∂b∂x+b∂a∂x

Q: B: Use the Chain Rule to find the derivative of f(x,y) xy with respect to (t) along the path y =…

A: Solution:-

Q: 9. For f(x) = arctan (2 sin ( Vx )) , compute the first derivative at the point %3D X =

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

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Q: Find the derivative of fuction Γ(z)=pinz+z^2   Γ'(z)=?

A: Here we have to find the derivative of τ(z)=πnz+z2

Q: The population of a city is associated by the function P(x,y,z)=x+2y² + 2z². If the population of…

A: It is given that Px,y,z=x2+2y2+2z2. The objective is to evaluate the greatest rate of decrease at…

Q: What is the derivative of x² + y² = 9 using mplicit differentiation? dx = xy dy dx = -xy dy dx dy dx…

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

Q: By using caushy Rieman find the derivative of f(z) =Iz| if it exit ® fLz) = 2 +Z1

A: It is given that the function fz=z. The function fz=x2+y2. Note that, If the function is…

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: What is the second derivative of y + Incosx = 0 * O (cos x) ^2 O 1 O (sec x)^2 tan x

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Q: compute th directional derivative of f(x,y) at point P in the direction of the point Q .

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Q: A bounded, 3B > 0 such that |f(x)| < B Vx € (0, 1), continuous function on (0, 1) with unded…

A: We will find an example

Q: The directional derivative of f(x, y) at the point (a, b) in the positive y- direction is f (a, b).…

A: Solution: We know that if f(x,y) is a function of two variables x and y, then fx at a point (a,b)…

Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure 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: B: Use the Chain Rule to find the derivative of f(x,y) = xy with respect to (t) along the path y =…

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Q: Find the directional derivative of f(x, y) = ln(sqrt(x^2+y^2))  at (x, y) does not equal (0, 0)…

A: Since we have to find directional derivative of function f(x,y)  at (x,y)  toward the origin-…

Q: W = у + 2z дz дудх' дх? ду

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Q: Find the derivative of the function f(z) = 3z² +7z at I = a.

A: Given,            f(x) =3x2 + 7x  and x=a

Q: Find the maximum directional derivative of the function f(x.y) = x In y + x2y2 at the point (-1,1).…

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Q: The directional derivative of f(r, y) =-e" cos y at (0, 5) in the direction of v = (-6, 8) is

A: Given that fx,y=-excos y at0,π4and v=-6,8

Q: dy by implicit differentiation of 2r2 3y2 = 4?

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Q: Find the gradient of the tangent line to the curve x² + y =10 at x=1, where y > 0. %3D

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