et w(x, y, 2) = x² + y² + 2² where z = sin(7t) , y = cos(6t), z = e". %3D dw dr dy dz by first finding dt Calculate & and using the chain rule. dt' dt dt dz dt dy dt dz dt Now use the chain rule to calculate the following: dw dt

Q: dy (b) Find ,where y = cos ecx –4 r +7 dx

A:

Q: y=sin(x−y)

A:

Q: cos 2x dx (b) 4 cos t dt 0 2

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: dy -y'sinx is: dx The solution of Select one: a. y3cosx+ C O b. %3D COSX-C C. V=3 CO5X + C d.…

A:

Q: dw Use the Chain Rule to find , where w = sin 8x cos 4y, x= dt , and y = t. dw dt (Type an…

A: Given w= sin(8x)cos(4y), x=t/2 , y=t3

Q: Find II. | arctan 4t dt

A: as per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

Q: find dy/dx and dy/dx2, if : x = a(cosθ + θsinθ) and  y = a(sinθ - θcosθ)

A:

Q: find ds/dt. s = t2 - sec t + 5et

A: Given: The function is,

Q: b.Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x,…

A: Given that, v=yxy=vx

Q: Evaluate sin 2t dt. t 8.

A:

Q: u(x, t) = ear+bt %3D 1 u(x, t) = -/at %3D

A: The given functions are ux,t=eax+bt and ux,t=1te-x2/at.

Q: dx dt 2w3 d. dw Sin (x)-InIxldx

A:

Q: Find dY for the function y= cos² 3X+ VSin x dx

A:

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.