For f(x, y) = sin(9ry), evaluate fa at the point (2,-). %3D -9 O s(2) -18 O (2=) - 97 o s.(2) =0 97

Q: Find impicitly, tf e*(eУ — 1) + sin(2x + 5у) %D In(V7) - - сot(2x) y+2

A: Given function is Differentiating with respect to x by using product rule ,we get

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A: Given,     y=cos4x

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Q: 4. If f (x, y) = sin(x)+e*y, find Vf (x, y).

A: Use gradient concept

Q: dy 7. dx cos(x + y), when x = 0,y = 4

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Q: Find for implicit function dx x² sin y + 3y3 = e5æ + 5

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Q: dy If x=5+ cos20 and y=3- sin20 , what is dx

A: We have to solve the problem

Q: Q1: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy? *

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Q: If f = 5x2y2 - XY2 then find af at (3,1) %3D dx

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Q: Q3.lf f(x,y) = sin²(x-3y)+sin(xy find: and af dy ax

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Q: y2 +Cos f (x, y, z) =

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Q: Let y f(x) be the solution of the equation 49 dy sin I dr uch that f(n) = 1. What is the value of

A: Here the given differential equation is a linear differential equation, so to find the solution we…

Q: -(sin(xyz)) = O xô zô y

A: Partial differentiation of the function with respect to x means to differentiate the function only…

Q: 4x + Vx Y = (a) 7x2 – 3 et (b) y = 7x³ cos x 19

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Q: 2 dy Is y = sin t, a solution to = 1 – y? Justify-

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Q: rcosA 2. r sin 0 dz dr de

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Q: Given that f(x, y) = xy sin(x + y).Find all second derivative fxx,fxy, fyy, fyx.Show all your steps.

A: Given: fx,y=xysinx+y

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Q: B) If f (x, y) = tan (2x – 3y) find дх ду?

A: Given function is fx,y=tan2x-3y

Q: For the equation y" + 4y = 0, (a) Show that y(x) = A sin wx + B cos wx is a solution for all values…

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Q: 4. Find when dx tanx a. y e, giving your answer as a function of y. b. y- In(xvx-1), x> 1 sinx-cosx…

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Q: What is if z = x²y+sin(ry²)? %3D dz = 2xy + y? sin(xy') az = x² + 2ay cos(xy) 8z = 2xy + y cos(xy?).…

A: The given function is z=x2y+sinxy2

Q: 2. If y = e-* cos 2x, then f'(x) = %3D

A: Given : fx = e-xcos2x

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Q: cos(x + y), when x = 0,y = dx 2 = dy : %3D

A: To solve the differential equation we can use a substitution u=x+y and then we can use variable…

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Q: cos(x) dæ with n = 4 is: The Trapezoidal Rule approximation for

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Q: y = sin(Ax + B)

A: We will find the Differential equation as following.

Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8)); i и

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Q: Find the value of zrr at the point (0, 3, 2) where x?y? + z2 – cos(xyz) = 10. -

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Q: F(x, y) = 3x – 4y3 + 5x°ys + cos(x) – 3 sin?(y) |

A: Given query is to find the partial derivative onnf the expression.

Q: if z=ex( x cos y-y sin y ), show that  ∂2z/∂x2+∂2z/∂y2=0.

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Q: etany) dy cos?(y)

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Q: Q10. If f(x, y) = cos( 3x + y) Find:

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Q: If f(x,y) = sin(2x+3y) then f yy

A: Given: A function fx,y=sin2x+3y fy is the derivative of fx,y=sin2x+3y with respect to y. And fyy is…

Q: tan (e) 1+z* (d) (22+ cosh 2z)dz () z coshz dz zp-

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Q: b.9f Fex)=x Sin lgix), where gL1)= , and g' (1)= -1, then f'(1)=2

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Q: Obtain the der a) cos(xy)=2y, find y'

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Q: e) Differentiate f (t) = (e-6t+ sin(2-t)) -9- %3D

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Q: cos y f(x, у, z) -D xz2 XZ

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Q: a) Prave that sinlx t Cos-lx = ½ %3D

A: To prove,   sin-1x+cos-1x=π2

Q: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy?

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Q: Find fur for f(x, y) = 7xe* y° sin (/x - 3x* +1)+9x°e"

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Q: Find F dX, where x= 3 cost y= 1+3 sin 2r)

A: Given It has to find line integral of given parametrically curves Where

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Q: dy 7. dx = cos(x + y), when x = 0,y == 4

A: Differential equations, with substitution method and separation of variables

Q: Solve the fo llowing D.- E y + y tan X Cos X %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.