2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin() sin)+3cos² -2sin2cos( A: -2sin2cos B:- ) 8y³sinz -2sin2cos cos()+2 sin) sin()+3cos C:- 5. 8y2sinz) -2sin".cos()+2 sin() sin(-)+3cos° +2 sin) sin)+3cos² D:- 5 8y sinz) E: none of above

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A: Given :fx,y=ln2xln3y+x-y-xy-3

Q: The derivative of the function y = (10e* – 10x*)(tan x) is: a. y' = (e* – 40x3) tan x + (10e* –…

A:

Q: 26) Find the partial derivative of of f= y cos x+ 2x sin z + 5y with respect to y.

A:

Q: Find the partial derivative of f (x, y) = e2+3y cos (x³y²) with respect to x. O fa (x, y) = e2x+3y…

A: Given f(x,y)=e2x+3ycosx3y2 To differentiate f(x,y) partially with respect to x Let u=e2x+3y…

Q: 5. Consider the function f(r, y) = sin(x² + y²). (a) direction of (4,3). Find the derivative of f(r,…

A: The directional derivative is the rate at which the function changes at a point in the direction .…

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A:

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Q: In Exercises 21–42, find the derivative of y with respect to the appro- priate variable. 21. y =…

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

Q: 8. Find the directional derivative off at the p in the direction of v = () of f(x, y, z)=x²exx, p =…

A:

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:

Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy² = 2 (C- cos x) O…

A:

Q: 3. Show that the complex function f(z)= cscz =1/ sinz satisfies the Cauchy-Riemann condition. Find…

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Q: Find all the second partial derivatives. T = e-4r cos(0) -4r 16e cos (0) Trr %3D Tre 4e 4"sin (0)…

A:

Q: 1 Find the direction derivative of f(x, y, z) = x²y -zx -y³x at the point (1,-1,1) in the direction…

A: Directional derivative

Q: Find both first partial derivatives. z = sin 5x cos 5y

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Q: 2. Determine the directional derivative for u = log, x2lnz if it is defined by the direction at dx =…

A: Given u=logyx2lnzby the direction at dx=dz, dydx=2and is situated at a point in the Euclidean space…

Q: Use your knowledge on Higher-order derivative and Chain Rule to show that z" + 4z' + 8z = 0 if z =…

A:

Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

Q: 4/(A)Find the derivative of f(x, y) = xe + cosxy at the point (2,0) in the direction. дz (B)If Z =…

A:

Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

A:

Q: Find the partial derivative of z with respect to x z = (3x² + 1) cos(x²y). əz = -2x (3x² + 1)…

A: Given function z=(3x2+1)cos(x2y)

Q: _6. What is the derivative of f(x) = (5 – x²)²? а. 2(5- х2) b. 10 – 2x2 C. 4x3 – 20x d.(5 - x?)(5 -…

A:

Q: u = xz siny + yz cosx + xy tanz

A:

Q: 7,2 Find the critical noint(s) of al r) and use the Second Derivative Test to classify the

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Q: If f(x,y)=3 sin (2x+y)-4 cos (x-y) then the second derivative f , is a. 3 sin (2x+y)+ 4 cos (x-y) b.…

A: In the question it is asked to calculate the double derivative of the function given.

Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy²= 2 (C- cos x) O y…

A: This question is related to differential equations, we will solve it using given information.

Q: 1. Consider the function g(x, y) = cos(xy) + sin(x – 2y) (a) Determine g (c) Determine (c) What is…

A: Given function is  g(x,y)=cos(xy)+sin(x-2y) we have to find the second order partial derivatives…

Q: Calculate differential: f(x) = e-* cos(3x) + 2 of the range [1,2] with h=0.05 Using the backward…

A: Equation is  f(x)=e-xcos(3x)+2.Numerical differentiation method to find the solution.The value of…

Q: For a function f (x, y), (0, 0) and (1, 1) are two critical points. Also, fxx = 2x², fyy = y²2 and…

A:

Q: (b) 22). Compute the partial derivative frryz for f(x, y, z) = cos(cos(x³ + z²)) + x² In(y² +

A: Given f(x,y,z)=cos(cos(x3+z2))+x2ln(y2+z2).We need to find the partial derivative fxxyz for the…

Q: Find the derivative of f(z) = In(z -+ O (A) f'(2) = 2² – 3z + 2i). | --2 V:-3:+2; 1 AB) ƒ'(2) = V-3:…

A:

Q: 2) Let f(x, y) = x sin(2y) + 5y¹. Find fyyyyyyyyyy (x, y) (10 partial derivatives), explaining how…

A: Here the given function is f(x,y)=xsin(2y)+5y4x. We have to find the 10 times partial derivative of…

Q: 2. Find the critical points of f(x, y) = x³ + 2y³ – xy and analyze them using the Second Derivative…

A:

Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y =…

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So…

Q: Find all the first and second order partial derivatives of f(x, y) = -4 sin(2x + y) + 1 cos(x – y).

A:

Q: 2. About what point is the local linear approximation l(x) 1 of the function f(x) = tan- x 4 valid?

A: Let's Solve,

Q: 5. (а) Find the directional derivative of f at P in the direction of ā if f(x,y) = y In(x) ; P(1,4);…

A: To find The directional derivative of f at p in the direction of a.

Q: is The third derivative of y = cos 3 1 sin 27 1 a) y" b) y" =- cos %3D %3D | - 3 27 3

A: The given differential equation is : y=cosx3   -1

Q: Find all the second partial derivative T = e-4r cos(0) -4r, Trr 16e 'cos (0) %3D Tre = 4e -4r,…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: (2.2) The directional derivative of f (E, y) at P(1,2) in the direction of i+j is 2v2 and in the…

A:

Q: Find the third order derivative of y = In(cos(2x))". A. y' = -40sec²(2x)tan(2x) B. y' = -80sec…

A:

Q: Find the derivatives of the f: 1. y: sin (x²+3) 6. y= e tan 3x 7. y: e 2. y= tan (4x*) cot (3x-8) 3.…

A:

Q: Find the third order derivative of y = In(cos(2x))5. %3D A. y' = -40sec² (2x)tan(2x) %3D В. у' 3…

A:

Q: Find the firsst derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and the first partial…

A: Given:       y=arctan3sinx4+5cosx First derivative:     dydx=ddxarctan3sinx4+5cosx…

Q: Find all the second order partial derivatives of the function : f(x, y) = In 4ry + sin 3ry + e4z-3y

A:

Q: Find all the first partial derivatives of z = a sin 3y – 2y? cos 3x (Choose all applicable answers)…

A: Using partial derivatives.

Q: Find all the second partial derivatives (including fxy etc.) a) v = sin(2s^2 − t^3)

A: Please see the explanation below

Q: af and дх if f(x,y) = 3x* – 5x²y + 3xy3 + Find %3| ду se sin xy2. x+2y Find the partial derivative…

A: Partial differential equations

Q: (b) Show that the function defined by xy √√√²+y² f(x, y) 0 if (x, y) = (0,0) is not differentiable…

A: We have to show that the function defined by…

Q: ди + 3x- = 1 + u, dx ди -co 0, dt u(x, 0) = f(x).

A: