O y'+ (oy -asin 8t y W): -1 2

Q: Find both first partial derivatives. 18y2 x az %3D ax dz ду

A: The given function is:z=18y2x

Q: Find the differential dy. y = 6x7 + 3x2

A: Given:y=6x7+3x2

Q: Ily approximate the differential dy when x changes from 64 to 64,07 Y

A: Since the student has posted multiple questions and mention to solve question numbers 1 and 2. But…

Q: Inx dx, 2. Integrate (1) using the substitution u = In x (ii) using integration by parts.

A: Integration by substitutions and by parts

Q: Compute the differential dy for y = -6x° + 8x5. dy =

A: topic - differential equations

Q: 2. 2. Let そニと X=UV, y = sin v, Use ナ chain chain Rule to find Ev.

A: 1) The given function z=e2x2y+3xy2 Differentiate with respect to x taking y as constant…

Q: Differentiate ysin(1/y)=1-xy

A:

Q: 4. |1- sin2y dy 6. y +2)/y- 1) dy (y + 2)/y

A:

Q: . Form the differential of the system of circles touching the y-axis at the origin.

A: The solution is given as

Q: 5. sinx+ cosh2y = 0. dy 6. /2xy -= 0. dy y

A:

Q: Find both first partial derivatives. sinh(5x + 4y) az %3D dz %3D ду

A: Explanation of the answer is as follows

Q: Find both first partial derivatives. z = cos(10xy) dz az ду II

A:

Q: Let y=5x^2Find the change in y, Δy when x=3 and Δx=0.2Find the differential dy when x=3 and dx=0.2

A: To find the following parts. 1.)find the change in y (∆y), when x=3 and ∆x=0.2. 2.)find the…

Q: Find both first partial derivatives. z = 13xy az az ду II

A:

Q: Evaluate: 1-11-24 = - dx 1 + x 0 By the trapezoidal rule with h = 0.5, 0.25 and 0.125 respectively.

A:

Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

A:

Q: integrate dy/(sb - smy-bny-nmy^2

A: SOLUTION-

Q: Find the total differential w = x2yz2 + sin yz

A: Partially differentiate w = x2yz2 + sin yz with respect to x and keep y and z as constants.…

Q: Find all the second partial derivatives. f(x, y) = ln(ax+by)

A:

Q: Find the partial derivative. z = sin(2.a*y – 3xy?) az

A:

Q: sinh (u+v)=sinhycoshr+ coshuxsinhv

A: Use hyperbolic function

Q: Find both first partial derivatives. z = sinh(7x + 16y) az ax az ду

A: From the given problem: z=sinh7x+16y As we know that: The chain rule: fgx'=f'gx·g'x The Power law:…

Q: By using chain rule Find dy/dx iff- u=-1, x=-1

A:

Q: Find both first partial derivatives. z = sinh(6x + 19y) dz дх dz ду

A:

Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

A:

Q: Estimate Ay using differentials. .1/3 y = x¹/3 e³x-1, a = 1, dx = 0.1 -

A:

Q: 1 J sec- ztan - zdz

A: Solve the following

Q: Compute Y (II) withe y" y'= -8 (Sinx+cosx. Y(T) = 0, y¹ (F) --8, by @ Taylor Series

A: Given differential equation is y''-y'=-8(sinx+cosx)     (1) and y(π)=0, y'(π)=-8 Solution a: Using…

Q: 1 of 1 dy -3-9x, y'6)=8, dx² ylo)=2 %3D

A:

Q: %3D

A: We are given: u=ln 1-t21+t2⇒dudt=ddtln 1-t21+t2 The derivative can be found as follows:

Q: d?x 2 dt2 dx - 5- dt 3x = -9t2 – 1 - %3| - - dx When t = 0, x = 1, = 0, find x when t = 2 %3D - dy

A: The given differential equation is 2d2xdt2-5dxdt-3x=-9t2-1                   (1) to find x(2) with…

Q: 3. f sin³y(2-3cosy)² dy

A:

Q: Find both first partial derivatives. z = sinh(7x + 5y) az ax az ду || ||

A:

Q: Intergrate dy (2y-x) =In Co)

A:

Q: tion to (1+ x²) dy + 2xy = 4 that satisfies the initial condition y(0) = 0. dx %3D %3D

A:

Q: Find both first partial derivatives. z = cosh xy2

A: Given: z=cosh xy2 To determine: ∂z∂x& ∂z∂y

Q: dy Use an appropriate technique to find dx from x² + y² = (2x² + 2y² -x)*.

A:

Q: 1. If y= tanx, prove that y"=2(y² +1)(3y² +1).

A:

Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution.

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: dy 3 (49-y²) 2

A:

Q: v = exy In(x +y)

A:

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

A:

Q: 1) (2cos³xsin x – ysin x – 1)dx – cos x dy = 0 ; when y ) = 3v2

A:

Q: Find the partial derivative. 2 = (r² + 5z – 6y)“ az ||

A: The given function is: z=x2+5x-6y4

Q: (b) Find the partial derivative, g where g(x,y)=sin' (2x+y). (c) Given z= In(2x+3y) with x 2s' (t-s)…

A:

Q: Find all the first partial derivatives of; glw,2, y, z) = xe2w - wyz?

A: Topic:- partial derivatives