4) x²y + xy² + xy = -1 ,y' at x = -1 %3D

Q: dy/dx if y=tan((1-2x)/(1+x)) dy/dx if y=x^4 ln(3x-1)

A: 1)    y=tan1-2x1+x2)    y=x4ln(3x-1) Hint:  Chain rule and then uv and u/v rule of differentiation

Q: 3. (4x³y5 sin 3x + 3x*y$ cos 3x) dx + 5x*y* sin 3x dy = 0 y(0) = 1

A:

Q: 7. Evaluate Soy4 2 - y dy using Gamma/Beta function.

A: The solution is given as

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

A: The given function is:z=18y2x

Q: (1) y = x³ lnx (4) y=²+1 (2) y = √sinh √tan.x -,u= u= 3x²-2

A:

Q: (1) Find the general solution for -) dx - -) dy = %3D

A:

Q: Compute dy/dx for the function. y = sinh 2 8x O 2 sinh 8x cosh 8x O 2 cosh 8x 16 sinh 8x cosh 8x 16…

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Q: 5 Find xy dydx. 4

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Q: 3. find dy/dx of y= sinh 2x

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Q: find dx/dt at x = 3 if y = -5x^2-4 and dy/dt = -3. dx/dt =

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Q: 2). 3rin y l dy dx [ 5 X In Xナ3

A:

Q: if: Determine dx 1.3 x'y' +x* coshy = 3 Use Partial Derivatives

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Q: Integrate SxIn x)dy

A:

Q: Differentiate implicitly to find the first partial derivatives of z                              x2…

A: Given that function, x2 + y2 + z2 = 1 Differentiate with respect to x on both sides,…

Q: Find both first partial derivatives. . z = ln x/ y

A: Given that z=lnxy

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

A:

Q: 15 dy dt 2-

A:

Q: Differentiate implicitly to find the first partial derivatives of z. 11x2 + 5y2 + 3z² = 100 az əx az…

A: Given,  11x2+5y2+3z2=100

Q: Find the indicated partial derivatives. y+ Sz az dy ex

A:

Q: Differentiate. y =x° In x- dy II

A:

Q: If y = eex the y' - y" + exy' is equal to?

A: The given equation is y=eex

Q: y ln x - x ln y = 1

A: ylnx-xlny=1Treat y as yx

Q: 7. Integrate em***)dx_using the Substitution method. x +3

A: To evaluate the given integral using substitution method.

Q: Find both first partial derivatives. z = 2y2√x

A: fx = differentiate with respect to xfy=differentiate with respect to yddxxn=n xn-1

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

A:

Q: y = x* Inx dy : =x³ +4x° Inx dx O Op tion 1 None of these dy - -x -4x° In x dx =x² -4x° Inx dx O…

A: Explanation of the answer is as follows

Q: 11. Find the length of the curve x = on the interval (2, 4] (integrate with respect to y) 12y3 un

A: Given that the function x =y55+112y3 Find the arc length of the graph of the given curve on the…

Q: Write in your words about some of the applications of the partial differential equations With…

A: Given :- some of the applications of the partial differential equations

Q: 6. Why is it very easy to conclude that x2 dx diverges without making any integration calculations?

A: This question is taken from the calculus and sub-topic is improper integral in which we have to give…

Q: 1- (x²1) + dy 2xy = 1 ty Cosx Ex Sinh 2- Sin(x) dy dx 3- - dy dx + 3x²y = x²x³ + 4- xlnx dy dy +y =…

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

Q: From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)

A:

Q: Find a result by using homogenous for (x³ - 3x²y)dx-(x3³ - y³)dy = 0

A: This question is based on solution of Homogeneous differential equation.

Q: Differentiate implicitly to find the first partial derivatives of z. 7x2 + 5y2 + 2z2 = 25 az ax dz

A:

Q: 5. The integrating factor of the di equation 2y dx + (x- x^3 y^3) O x*3 y^2 O Does not exist

A:

Q: Find dy/dx 1. y = sin ( 5x - 9) 2. y = sin-4x/5

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Q: 5/(A)Evalute ex² dxdy. (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

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Q: Find dx dt dx dt at x 2 if y= = - 2x² - 1 and dy dt = - 3.

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Q: Find both first partial derivatives. z = In əz əx az ? ду II

A:

Q: find dy/dx of y=sin^2 4x+1/2 cos 8x

A: Given,         y=sin24x+12cos8x

Q: dx 25. Integrate: S Ve-2x –1 А. Sec-1e* + С В. Sec-1е-* + С С. — Sec-1e* + С | D. —Sec-1e-* + с

A:

Q: Find both first partial derivatives. z = ln√xy

A: Given  z = ln√xy. We need to find both the first partial derivatives of the above function.

Q: If z-f (x y): then its total differential can be expressed as * (),中 (). dyds dy + dz O Option 2 O…

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

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

Q: Find dy dy dt at x = z - 1 if y = -5x² + 3 and dx dt 5.

A: topic:- derivatives

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

A:

Q: Find explict solution of the foilowing initial-value problem dy yoanx?, yla)of %3D dx

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Q: 2. ху 4 a. when x=8 10 dx b. when x-1 dt dy dt -6

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Q: (In x) dx Integrate: 1

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Q: Find at x = -2 if y = - 4x² + 3 and dy dt dy dt = dx dt - 1.

A: Topic = Derivative As per guidelines , at a time only one question can be answered. pleas repost for…