dy ifx²y + secy Find dr In x .

Q: dt 34. tan t/4 – sin² t dy - Vy dy 35. 36. yV3 + (In y)? x² 1 38. dx 4х + 5 37. :dx /x² + 2x + 5…

A: 34) Solve the integration:

Q: if x²+y²=t-- and x*+y*=t*+÷,prove dy dx x'y

A:

Q: f(x.y) =e^sin(y) + In(xy) ; әз of Әхд-у

A: Given: fx,y=exsiny+lnxy To find the partial derivative of ∂3f∂x∂2y Partial differentiation: Partial…

Q: Find dY at x = -1ifY zu%5V=4 3. and u= X²+ X

A: Given that y=u3+5u-4 and u=x2+x We need to find dydx at x=-1 Take y=u3+5u-4 Substitute "u"…

Q: dy/dx= tan^2 (x) / sec^2 (y), y=pie/4 when x=0

A: given,                 dydx=tan2xsec2y and           y   = π4 when x =0

Q: dy/dx= tan^2x/sec^2y when y= pie/4 and x=0

A: Given dydx=tan2xsec22y   y=π4 and x=0

Q: (c) Show that (d/dz)z does not exist anywhere,

A: See the attachment

Q: Find S (x + In y) dydx

A:

Q: af dy of f(x, y) = tan (x²y³ + 2xy)? What is the

A: Given:     To determine:

Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); fi-) U =

A: we can solve this as follows:

Q: 3 If y= Vx (x-1), find dy (Use rules, not a de finition XP

A: Given:         y=xx-1       dydx=ddxxx-1    Apply product rule:         ux·vx'=u'(x)·v(x)+u(x)·v'(x)…

Q: (a) i. Find Re{sec (x + iy)}.

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

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

A:

Q: For the relation siny – y² =x²y– x+x , is dx 3x²y+1 А. cos y – 2y –x T – 1 3x² + 2y – cos y cos y –…

A:

Q: a Ex Let mxy+2), x=Git, yosint Find dw at t:3.

A:

Q: (b) If f (x, y) = y sin2x + x°cosy °cosy 3 then verify dxðy dyðx

A:

Q: QS A) Find IF y = - Ve IF y =-Vt and t sinx

A:

Q: dy If y = 2sin 3t then aY is: dt

A: we know that, derivative of a^x = lna * a^x  so from this we will solve the quesiton

Q: What is the difference between dy dy and Ay Use an example y = 4x?+ eX to under stand. 4x2+ ex

A: In the given questioin we have to tell about the difference between dydx,∂y∂x and ∆y∆x. first we…

Q: find dy>dt.…

A: Given function, y=ecos2pt−1

Q: Solve the Ro liowing B E 2 X + 2 -zey= zX

A:

Q: Find the general solution: dy = tanxtanydx %3D

A:

Q: 1. a.) Use use the L’hospital rule lim(1+* dy b.) Use Devirative Rule to search dx from the equation…

A:

Q: If f = 5xy2 - X³Y then find df at (1,1) dy %3D

A:

Q: B. Find y). 1. y = cosh?x 2. y = x tan-1 x - In vx2 + 1

A:

Q: [-+] 5t dy 3.1는-51%3D-y dt

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

Q: determine dy/dx if xy = ecsch(x)+πcos(0)

A: Given, xy = ecsch(x)+πcos(0)

Q: 9. Find dy for y defined implicitly. by the equation xy-secly)-3x

A:

Q: If f(x,v) = ex In(5xy) find dy?

A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

Q: Find dy/dr by differentiating implicitly if z +ry- 6r = 2.

A:

Q: Finf y' if x=Arccos(1-t), y=/2t-t2.

A: We can find the answer using chain rule as below.

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

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: Hw z] Find Sxsin(x)dx using this rule.

A: Given that, Using the chain rule, The integral becomes,

Q: OSS T (x+y2) dydx

A: When the region of a double integral represents a circle, it is convenient to use polar coordinate…

Q: If y = V1-x² sinx, prove that (1–x²) +xy =1– x². dx

A: Given that :- y=1-x2sin-1x Prove that :- 1-x2dydx+xy=1-x2

Q: dz az B. Find əx and ay 3. x eY+ cos xy36xz+5x²

A: partial derivative

Q: If x2 + y2 = z2, find dy/dt when x = 3, y = 4, dx/dt = 6, and dz/dt = 6.  (Enter your answers as a…

A: We would differentiate the given expression implicitly w.r.t. t, ........................(1)

Q: dz and ду dz Find z = x° In (1+ xy° dz az dy

A:

Q: 2. Show that the function u = p(xy) + Vxy v(y/x) provides the equation = 0. dy? -

A:

Q: dy Find for x=secy dx A xsinx B D 1-x?

A:

Q: Given x²y3 = In(xy) Show (using complete solution) if the equality below holds dx (x\(3x²y3 – 1) dy…

A: Using differentiation

Q: Prove that (y – æ)(y + 3x)³ = cx° is a solution to 3x2 – 2xy + 3y² )dx = 4xydy.

A:

Q: If y= V (x-1), find dy (Use rules, not a de finition ) Xp

A:

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

A:

Q: sec y Then y8 Let z dz dy y16

A:

Q: Find, if y (3 z)t* + cosec (t) + Z In(2t + 3) dt2

A: First of all, let's get rid of Z by substituting Z = 43 in the equation above: y = (3 x 43)t4 +…

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.