1-fd dydx R = {0,1} * {2,5} y2 2-S y2 (1–5x)2 dxdy R = {0,1} * {0,2}

Q: The standard form of 3dy – xydx = 3y³e¹x/³ by Bernoulli's equation is: dx A d 2=3e dy ху B D…

A: Solution : Given that

Q: (a) By using thẻ chain rülé and the dérivative (1, (1xl) = {"1, if x>0 if x<0' d %3D dx 1-1, find -…

A:

Q: 20) Let y=7x+5x Then compute dy and Ay for X= -7 and dx =0.4. dy =? and Ay = ? Gounded 6o 4 decimal…

A: Derivative: - The derivative of the function is the equation that we find. The instantaneous rate of…

Q: Find the particular solution of y (9x - 2y) dx -x (6x - y) dy=0., when x=1, y=1. Let x=vy

A:

Q: dy dt (d) di² + 2- 3— 3t + 2, у(0) — У (0) — 0. dy (е) di? dy + 20y %3D —3 sin 2г, у(0) %3 у' (0) —…

A:

Q: Let f(r, y, z) = ln(x² + z) + y²e#² – cos(2yz). Find fzyr- %3|

A: Consider,                                                                 f(x, y, z) = ln(x² + z) +…

Q: • If u = x+ 1 t= yu y = -t² then, %3D 1. dx dy -1 dy = X dx dy 3. dx |3D dy 4. dx 1 O 2 O 3 O 4 O 1,…

A:

Q: Can you help me step by step?

A: Differentiate both sides w.r.t. t. Apply product rule on the right side. Product rule: (uv)'=u'v+uv'

Q: Find d3f where f(x, y, z) = ln(x + y − z) + cos(x2y)

A: As per the question we are given a multivariate function as : f(x, y, z) = ln(x + y − z) + cos(x2y)…

Q: (xy² + 3y²)dy – 2x dx = 0 is not separable. ylgn ihi

A:

Q: dz Suppose that z = x³ – 3y?, x = 4(t³ – 1), and y = Int. Find using the Chain Rule. dt %3D -

A:

Q: Transforming A S B © D dx secx + 1 7 dz 1-2² 1==323d² -dz 1+z² [1+2²21 2-272 1+z² -dz -dz using…

A:

Q: - Find dy at x = -1 if y=u³ +5u-4 and u = x² + x. dx

A:

Q: dx If x2 + y2 + z2 = 9, dt dy 6, and dt dz when (x, у, z) %3D (2, 2, 1). dt 3, find %D %3D dz dt II

A:

Q: when (x, y, z) = (2, 2, 1). dt dz dy If x2 + y2 + z2 = 9, dx 8, and dt 4, find dt %3D %3D %3D dz dt

A: differentiate the given function with respect to 't' 2x dx/dt +2y dy/dt +2z dz/dt =0 Now substitute…

Q: If f(x, y) = 4x² – 6y², then the total differential of f at x = 1 and y = -2 is : O df = 24 dx + 8…

A: df=dx+dy (see step 2).

Q: B. Let z- ( x-y)exy Show: Zxx + zyy + e x9 Cy 3- x³)- -z (xy+ 2)

A: Given that                       z=(x-y)exy

Q: dx If x2+y2+z2 = 9, dt dy = 6, find dz when (x, y, z) = (2,2,1). dt 4, dt dz dt when (x, y, z) =…

A:

Q: 3. (4r'y-15r-y)dt + (r +3y-1)dy = 0 CS Scanned with CamScarner

A: We can solve this using exact equation of differential equation

Q: [-+] 5t dy 3.1는-51%3D-y dt

A: This is a linear 1st order differential equation.

Q: If x, y, and z are lengths of the edges of a rectangularbox, then the common length of the box’s…

A: Given- s=x2+y2+z2 To find- dsdt in terms of dydtand dzdt, if x is constant. Concept Used- As the…

Q: 1 z = Vuv, u = 3xy + 2x2 + e"-Y Find zzy at x = 1, y = 1

A: Topic:- function

Q: If f(x, y) = 2x² – 8y², then the total differential of f at x = 1 and y = -2 is : df = 32 dx – 4 dy…

A:

Q: dy 2. if y = In(x² + 1) Then at x=1 %3D dx 2- 2 In 2 2- 1 1- 4- 1/2

A:

Q: dy (3) If y = | (t – 1)²dt for x > 0, then compute dz In z

A: fundamental calculus theorem 2 states that if f is continuous on [a, b], then  ∫abf(x)dx=F(b)-F(a)…

Q: 6 If the substitution y = xº is made, the 64 3√√y 3 + √√y integral [ 1 dy will become

A:

Q: - Find the total differential df of f (x, y) = (x² + y²) 3/2.

A:

Q: -7x f(x, y) = e" sin(4x + 5y) af e^(-7x)(4cos(4x+5y))-7sin(4x+5y) af 5e^(-7x)cos(4x+5y) dy ||

A: Partially differentiate with respect to x and y by using product rule.

Q: d dt dx dy ruations dt - 2x +2y 1-2t, dyx-0. Giv dt 2 dt

A:

Q: If x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 2, and dz/dt = 2. (Enter your answers as a…

A:

Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: Find dy at x = -1 if y = u’ +5u – 4 and u = x² +x . dx

A:

Q: dy for 2xy - 4x +2y3 = - 32, with the conditions dt dx 3 - 4, х%3D2, у%3 -2. Assume x and y are…

A: 2xy-4x+2y3=-32 Differentiating with respect to t, we get…

Q: O from the equation z = In(x² + y²) + Zyy Show that zxx %3D

A:

Q: JS xy dA R: rectangle with vertices (0, 0), (0, 3), (5, 3), (5,0) 166xx 16 xy dx dy = xy dy dx =

A: The solution is given as

Q: LLL- (x+ y+ z)dydxdz. -1 J-1 J-1 |

A:

Q: If f(z,y) = 3z² - 8y, then the total differential of f at z =1 and y = -2 is: %3D O df = 6 dz + 32…

A:

Q: dy for 2xy - 2x + 3y3 = - 42, with the conditions dt dx 3 - 12, х%3D3, у%3 Assume x and y are…

A:

Q: The standard form of 3dy- xydx= 3y e* 4x/3 by Bernoulli's equation is: dx = 3e /3,3 ху A dy B y…

A:

Q: 14. Evaluate 4y dx +3ax dy, where C is the trapezoid with vertices (0,0), (2,0), (6,2) and (0,2).

A:

Q: 3. Use chain rule to find given w = Vx2 +2y2 + z² and a cos (st), y = -2s In t ane 2 = 3s?Vt. 3s2Vt.

A: Follow the procedure given below.

Q: dy dæ at x = 2 if y = 3x + 5 and dt Find - 2. %3D %3D - dt dy %3D dt

A:

Q: xy*-dy = (a* lIn a – y (а* In a - y %3D

A: we have to find the differential of ax=y

Q: 1 find the total differential dz. z=xsin y + x² z = (2x² + 3y)² z=5x-7y

A:

Q: - = 2x, – x, dt dx, =-x, +x, +4e' dt

A: integrating, x1= (x1)^2-dx2/dt, replace dx2/dt with -x1+x2+4e^t in above equation…

Q: Assume x and y are functions of t. Evaluate DY/DT for 4xy-4x + 6y^3 = -258, with the conditions…

A:

Q: 24. Evaluate . (x – y) dx + (x + y) dy counterclockwise around the triangle with vertices (0, 0),…

A: Given integral is, It can be represented using Green's Theorem as,

Q: 6. If z2 = x2y2 (where x, y, and z are positive), and dz then what is when x = 2 and y = 3, given…

A: Given problem:- If z2 = x2 y2 (where x, y, and z are positive), and dz/dt then what is when x = 2…

Q: dw t- dt dw + x- dx 1, -0 1, w(х, 0) %3D f(x). ||

A:

Q: Find dy/dx if y = x by using the Chain Rule with y as a compositionof y = 1 + (1/u) and u = 1/(x -…

A: