dy e: Find for the following functions: - dx 1) y = Vx + 8Vz – 2

Q: 4. Evaluate: S. yx?dx + xzydy + xz²dz, where C:x = sint, y = cost, z = t2 , (0 st< 1).

A:

Q: Find dy/dæ in terms of t if x =t – t°, y = 2+ 4t dy/dx =

A: The differentiation of parametric form of functions can be done by using the formula,

Q: dy Given y = In(tan 0), find 0 such that 4, where 0< 0 <T 2

A:

Q: M(x,y) dx + (x,y) dy=0 to be exact

A: Solution :

Q: Find dy/dx, where y is a function of u such that dy/du = u/(u2 + 1). State the answer in terms of x…

A: we need to find dy/dx, Where y is a function of u such that dy/du = u/(u2 + 1)...(1). State the…

Q: Find dy/dx and d^2y/dx^2 X=t-e^t, y= t+e^-t For which values of t. Is the curve concave upward?

A: Given that, x=t-e^t, y= t+e^-t

Q: Identify an inner function u = g(x) and an outer functiony = ƒ(u) of y = ex3 + 2x. Then calculate

A: It is the composition of two functions, namely Inner function: Outer function:

Q: Find dy/dæ in terms of æ and y if æ°y – x – 2y – 1 = 0. dy dx

A: We have to find dydx in terms of x and y if x3y-x-2y-1=0.

Q: dy Os:A- Find dx for the following functions: - xy? 1- 1+secy = 1 + x* 2- If y = and t = V2x+1 12+1

A: NOTE- SINCE, WE ARE ALLOWED TO ANSWER ONE QUESTION IN ONE SESSION. SO, I HAVE ANSWERED FIRST…

Q: dy 28. (i) Find , where a) y= In b) x+y+ cosxy = 0 dy (ii) Given that x= e'cost and y=e'sint, find 2…

A: As per the guidelines we can solve the first three subparts or first one question. If you want more…

Q: Find the extremal of the functions using Euler's equation. [²(x² + y² (y2 + y² + 2ye*)dx, y (0) = 0,…

A:

Q: Find dy/dx, where y is a function of u such that dy/du = u/(u2 + 1). State the answer in terms of x…

A: Given: dydu=uu2+1. u=x2+1 By using the chain rule, dydx=dydu×dudx       =uu2+1×ddxx2+1…

Q: dy Find for the following function. dx y= 2x sin (x2) dy %3D 2 dx

A:

Q: Given dy dy +2- dx + 5y = e and y(0) = 0 and = 0 find the value of y(0.1) and y'(0.1) using the %3D…

A: Hi! You have posted multiple questions. As per norms, we will be solving only one question. We will…

Q: ;(y+ 1) e*dx = (e* + 1)y dy, what is F = 1.F. J (-e*y - y)dy? %3D

A: Given: y+1exdx=ex+1ydy

Q: Given a+ yx = e¥ , what is 1-y dy dz 1+y dy 1+y dz 1+y el-I

A: Given equation is x+yx=ey We have to differentiate the given equation. To differentiate given…

Q: dw by using Chain Rule. (Your answer should not include z ond y. dt = z+v? z = cost + sin t and y=…

A:

Q: dy Os:A- Find for the following functions: - dx 1- 1+secy xy2 = 1+ x* t2 2- If y = and t = V2x + 1…

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

Q: Find dy/dx, where y is a function of u such that dy/du = u/(u2 + 1). State the answer in terms of x…

A: Find dydx.

Q: Consider y=(x2+1)2x a) find dy/dx b)Evaluate y'(1)

A:

Q: dy -from the function y= sint, x= cost as a parameter. da? Obtain

A:

Q: dy Find for the given function. dx y = x° + sec æ – 1 dy Preview dx ||

A: y=x3+sec x -1  dY/dX=d(X3)/dX  +d(sec X)/dX  +d(-1)/dX           =3X2  +  sec X. tan X

Q: dy Find for the functions x = a(cost + tsint) , dx y = a(sint – tcost)

A:

Q: where t is a non-zero parameter. Show that dx 28 Given that x=z and y==. 1+r Hence find its value at…

A:

Q: dy Find for y = /12+13t dt. dv

A:

Q: (e) dy if y = (t +1)(t + 9) %3D dt It%3D3

A: Given that y=(t2+1)(t+9)

Q: dy Assuming y is a function of x, find for Rx sec(y) – 3y sin(xy) = e*xy. dx Note: R = 33

A: Given 33xsec(y)-3ysin(xy)=e33xy ....(1)

Q: dy Find for the following function. dx y=x cos x sin x dy %3D dx

A:

Q: dy If x = t – sin t and y =1- cost, then find at t = %3D dx a. -2 b. 0 С. 1 d. 2

A:

Q: dy Q:: Find for the following functions: - dx 1) y = Vx + 8Vz – 2 - 2) x³. y2 = 2x + 2y3 3) y =…

A:

Q: Compute xe" dx + x?y dy along the curve x 3t, y = t2, 0 < t < 1.

A:

Q: Find the value(s) of dy at y=1 given that x²y+y² =5. dx only only D

A:

Q: f x = sec(z) and y = tan(z) , then dy at z = dx 4

A: We can use the chain rule of derivative in order to solve the given problem.

Q: dx Find the value of at y=1 if x=z³+4z and z= dy (y? + 2y)²/3.

A: Given,         x=z3+4z  and  z=y2+2y23

Q: if y=tan u, u=v -1/v and v=ln x, what is the value of dy/dx at x=e

A: We have to find dy/dx .

Q: dy Given that y = In 9x, find dz dy

A: Use derivative rules to find dy/dx

Q: dx Find the value of at y-1 if x-z+5z and z= dy (y? + 2y)2/3.

A: x=z3+5z  &amp;  z=y2+2y23 Now put z=y2+2y23 in x=z3+5z, we get x=y2+2y233+5y2+2y23⇒x=y2+2y2+5y2+2y23…

Q: dy If x = t+sin t and y =1+cost, then find at t = dx O a.-2 O b. 2 O C-1 O d.0

A:

Q: dy a. Assuming y is a function of x, find dx for Rx sec(y) – 3y sin(xy) = eRxy. %3D

A: To find dy/dx

Q: dy Find for the following function. dx y = 9 cos x sin x %3D dx II

A: Given y = 9 cosx sinx  Find dy / dx = ?

Q: Given the implicitly defined function sin(r²y³) + y³ = r + y I dy dy and dx2 find at the point (x,…

A: Topic = Derivative

Q: dy Given the equation y In (x* +y +5) = 7, evaluate Assume that the equation implicitly defines y as…

A:

Q: w = xy +z xr = cost y = sint z=t a) Find at if

A: We have  w=xy+z x=cos(t) y=sin(t) z=t We have to find ∂w∂t

Q: dy Using the product rule for the dx function y = e3" sin x is equal to

A:

Q: dz Given z = e* sin y,x = u² + v²,y = uv, find dv

A: Using chain rule of derivative,

Q: Given x = 61 sin t + 36 and y = 3721 cost – 29 - dx (i) dt dy (ii) dt dy (iii) dx

A:

Q: Given the equation y In (x+y" +9) = 5, evaluate dy Assume that the equation implicitly defines y as…

A: The given equation is  y.ln(x3 + y4 +9) = 5 To find dy/dx

Q: Assuming y is a function of x, find dy/dx for 5x sec(y) – 3y sin(xy) =e^(5xy)

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.