dy B] If y = e" In(u) and u = V1-x2, Find dx

Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

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Q: Let y = x. Find dy and Ay at a = 8 with dx = Ar = 1. dy Ay =

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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 satisfies dx? 2 iven by

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Q: dy Find da if y = In(xiV1+ z° dy %3D dx

A: Recall: d(u.v)dx= u dvdx+dudx v d(xn)dx= n xn-1 d(ln x)dx=1x

Q: dy Let y = f(x) such that In(x – y) = 2x – y + e². Find dx

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Q: b Let y = x²sin(y) + yeXy, where x = s + 2t and y = st dv when s (ii) dt = o and t =1 is [d]

A: Find your answer below

Q: dy If x = t - t3 and y = t2 - t, the value of at t = 2 is %3D %3D dx

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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 is let y = (sin æ)*an 7 then dx

A: Given

Q: dy is let y = ln(V – 9 + a). -9+x then dx S'

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Q: u + c. Evaluate So (2x- y)3e dx dy with y = v, x= u-

A: To evaluate ∫02∫y22+y22x−y3eydxdy with y=v, x=u+v2.

Q: If x = 2t2 +t+1 and y=8t3+3t? + 2 then dy at t = 1 is dx

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Q: dy Given that y = 5u+ 4 and x = -u', hence find dx

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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 +y de : 2 et dx Arowar 1- ye" (c -x*) 1= yet (c -x*) %3D

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Q: (a) Let I = dx. Show that I² = dx dy. R2

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

Q: Let Z = In X - y dz Find and dx dz dy

A: I have given the answer in the next step. Hope you understand that

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: If f(x,y) = e* cos y then fyy (0,) is fyy (0) is

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Q: Find dy du du dx dy when y and u are defined as follows. dx u = 3x - 9x² and y = √u

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Q: Given x 13 In(t) and y = 169 t2 then find %3D dy dx dy dæ?

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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: || (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 dy/dx in terms of a and y if arctan(x'y) = ry. dy %3D dx

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Q: 2. If f(x,y)= te Vy of=D0 then show) that 49 c) of af =0 dxay

A: Consider the given function. fx,y=1yex-y24y (i) First, we have to show that ∂2f∂x2-∂f∂y=0. First,…

Q: If x= 2t +t+1 and y=8t+3t+2 then dy at t=1 is dx

A: We have to find value of dy/dx at x=1.

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

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Q: Given x = 8 In(t) and y = 64 t² then find dy %3| dx d²y %3D dx? ||

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Q: dy If y = (In x) (sin x), then dx

A: y=ln x(sin x) To find dydx

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

A: We can make it easier for you

Q: 2 In(t) and y=4 t2 then find %3D %3D dy dx d'y dx2

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Q: Find dy du dy and when y and u are defined as follows. du dx dx y = 3u² + 6 and _u = x² + 2

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Q: 1. Obtain the par hicul ar foluhon 4 DE . 9xy dy a. oy dx = ; uh en x= 2,y=1 b. 4xy dy = 2y (I+ y?)…

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Q: Given that y + x + cos(xy) = 0. Show that dy/dx = ysin(xy)-1 /1-xsin(xy)

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Q: Assume w = x²y*, where x and y are functions of t. Find dw/dt whenx = 3, dx/dt = 2, dy/dt = 4 and y…

A: To find the derivative of the given function w,  we need to apply chain rule of differentiation and…

Q: dy (a) Find if y = (In x)=². dx

A: For (a), dydx=lnxx2'       =ex2lnlnx'        =ex2lnlnxx2lnlnx'        =ex2lnlnx2xlnlnx+xlnx…

Q: y = x*, d'y 1 dy dx y dx, Prove that Y = 0. X

A: First we find out dy/dx then d2y/dx2. And put the values of dy/dx and d2y/dx2 in given condition.

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

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Q: Find dy/du, du/dx, and dy/dx when y and u are defined as follows. and u = Vx + 3 V = - dy du du dx 3…

A: Trigonometric identities: 1.d/dx(xn)=nxn-1 2.d/dx(constant)=0 3.d/dx(root x)=1/2root x And given y…

Q: u2-1 Given y = dy and u = Vx2 + 2, find dx %3D u3+1

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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: dy Given that y = x°e", find dx dy dx

A: In this question, we need to find the derivative of y = x9ex

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

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Q: dy If y = e" In(u) and u = V1-x2, Find dx

A: y = eu ln(u)       and   u = 1-x2 dydx = ?