Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

Q: Suppose y = v2x + 1, where x and y are functions of t. dx = 9, find dt dy (а) If when x = 4. dt dy…

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Q: f(x,y) = =dt V11-6t?

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Q: Give xy+x^2 y=2 such that dx/dt=2 in/sec. FInd dy/dt for x=1

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Q: dy If y = (t + 6t + 4) (3t2 + 4), find dt dy %3D dt

A: it is required to find the derivative.

Q: Let f (x, y) = 3x2 + 2xy + 5y. (a) Calculate df/dx (1, 4). (b) Evaluate df/dy at (x, y) = (1, 4).

A: Differentiate the function f with respect to x treating y as a constant to calculate ∂f∂x.

Q: Find the differentlal dy of the glven function. (Use "dx" for dx.) y = BVx + dy =

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Q: dz dz Calcula y dy z = x In(y) az = In(y) 1

A: Given : z = x ln( y ) To Find : ∂z∂x, ∂z∂ywe have given four options to determine the correct option…

Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: Given: y=7x-1 We know that ddxxn=nxn-1                                                       ..1

Q: Evaluate /// (x + y – 5z) dV Where - E = {(x, y, z) | - 6 < y < 0,0 < ¤ < y,0 < z < x + y²}

A: The given integral is: I=∫∫∫E(x+y-5z) dV where E=(x,y,z) | -6≤y≤0,  0≤x≤y,  0&lt;z&lt;x+y2

Q: Where f(x, y) y calculate (–1, 1) towards the point dv (-1, 3)

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Q: Find the differential dy. y = 5x2 / x-9       dy =

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Q: dy If y = (t + 2t + 8) (6t² + 6), find %3D dt dy dt

A: The given question can be solved as shown in step2.

Q: Find fr and fy- S(x, y) = /"9e" dt f.(r, y) : %3D f,(x, y) =

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Q: use Separation of Variables to find the general solution. dy/dt= y tan t

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Q: integrate ƒ over the given curve. ƒ(x, y) = x3&gt;y, C: y = x2/2, 0 &lt;=x&lt;= 2.

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Q: suppose y = √(3x + 1), where x and y are both functions of t. If dx/dt = 2, find dy/dt when x=5

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Q: find both dy/dx (treating y as a differentiablefunction of x) and dx/dy (treating x as a…

A: Differentiating with respect to x, we get

Q: Find the integrating factor of x dy / dx =x^ 2 +3y,

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Q: Compute dy/dx using chain rule where y = (u^2+2u)/(u+1) and u = x(x + 1)

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Q: If f(x, y) = xy + 3xy2 then df find at (1,2). dy

A: The function fx,y=xy+3xy2 then we have to find ∂f∂y at 1,2.

Q: Assume w = x2y4, where x and y are functions of t. Find dw&gt;dt when x = 3, dx&gt;dt = 2, dy&gt;dt…

A: Given:  w = x2y4, x and y are functions of t  To Find: dw/dt when x = 3, dx/dt = 2, dy/dt = 4, y = 1

Q: Find dy/dt of y = Ssin (cost) and simpli -t -cos t cos t V1-? the

A: Given:- y=sin(cos-1(t))  To find:- y'

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: Show that the function y(x, dy/at = a2y/ar2 = dy/ax = %3D %3!

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

Q: Xyz f(x.y.z) = function is given dt P(2,t,) in point fax + fy + f2z colculate.

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Q: Find of / dx and of /ay. f(x.y) = elx +y+6) of I dx = of I dy =

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Q: If y = 3x3 + 2x and dx 5, find dy when x = 2. %3D %3D dt dt dy dt %3D

A: Given, y=3x3+2x  and dxdt=5 We have to find dydt when x=2

Q: || (z, y) dy de = f(r,y) dx dy 0. Jo Jo O Tryc

A: Solution: The objective is to select the correct option

Q: Find fr and fy- f (x, y) = 4etlo dt f#(x, y) f„(x, y) =|

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Q: Let f(x, y) = 7e2" sin(5y) af af dy

A: We can make it easier for you

Q: If f(r, y) = 3x2 – 8y, then the total differential of f at z = 1 and y=-2 is: %3D O df = 6 dx + 32…

A: we can find the total differential as below using the properties of partial derivative

Q: dy - f *P, = 7 dt y(0) = 4.

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Q: Assume that x and y are differentiable functions of t. Find  dx/dt given that x= -3 , y= -2 , and…

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Q: z = √xy, dz dt t², y = -t² then 2 2 2t²) =?

A: We have to choose the correct option from the given options according to the given information

Q: What is the I.F of dy/dx = y - xy^3e^(-2x)?

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Q: If f(x, y) = 3x? – by, then the total differential of f at x = 1 and y = -2 is : O df = 24 dx – 6 dy…

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Q: Assume that y=5x and dx/dt = 8 find dy/dt

A: Differentiate by chain rule : →f(g(x))dx = d(f(x))d(g(x))×d(g(x))dx.

Q: dy If y = (t + 6t + 5) (6t² + 6), find dt dy dt ||

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Q: Find dx/dt. Uince x² + y^ = 225, then. 2x dx dt 2y.dy 24- ニ

A: Given that x2+y2=225 we have to find the value of dxdt.

Q: aw nd dt in term of t, if w = xy, x = cost and y = sint, when t = - %3D

A: Question 4 is not complete.  I am answering Question 5.

Q: What is the I.F of dy/dx=(y+y^2)/x?

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Q: If f(x, y) = x cos y + ye", find the second-order derivatives %3D af a²f ах ду" and ar" dy ax'

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Q: dy Find given that dt x² + y² = 2x + 4y, x = 3 y = 1, and dy = | dt dx dt = 6

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Q: D SS f(x,y,z) dV = f(x,y,z) dx dy dz

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Q: Show that f(x.y) dy dx= ,f(x,y) dx dy. ||

A: Order of change of integrals

Q: Assume x and y are both differentiable and functions of t. dy when x dt dx = 3? dt If y = x², what…

A: Explanation of the answer is as follows

Q: Find fr and fy- f(x, y) = fetlo dt f.(r, y) = fy(x, y)

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Q: Obtain the general solution using separation of variables dx = t(1 + t²)sec²x dt

A: Given: The differential equation dx=t1+t2sec2x dt . The given differential equation can be…

Q: Admit that for all (x, y), af (х, у) — х dx se (x, y) = 4y ду calculate g' (1) = f(2 cost, sint).

A: We have to prove 4y*f'x - x*f'y = 0 Also calculate g'(t).

Q: Find of/ dx and of /dy. f(x,y)= e(x+y+ 4) of/ dx = %3D of / dy %3D

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.