If y is a differentiable function of u, u is a differentiable function of v, and v is a differentiable function of x, then dy dy du dv dx du dv dx

Q: Express the relationship between a small change in x and the corresponding change in y in the form…

A: Consider the given function

Q: Evaluate: a In(x + y) e-y. dy dx

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Q: If y is a differentiable function of x and x^3 + 2y^3x^2=8y^2 Then find dy/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: we need to find dy/dx, Where y is a function of u such that dy/du = u/(u2 + 1)...(1). State the…

Q: Suppose y = (x + 1)5, and both a and y are functions of t. If. dy :1, find dt dx when x = = 1. |3D…

A: Given data:   The given function is y=(x+1)5. The first value given is dy/dt=1. The given value of x…

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

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Q: • If u = x+ 1 t= yu y = -t² then, %3D 1. dx dy -1 dy = X dx dy 3. dx |3D dy 4. dx 1 O 2 O 3 O 4 O 1,…

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Q: (i) dy x+y G@s x | + Sin x de

A: As per our guideline, i have solved only 1 question (ii)

Q: .If y = f(u) and u = g(x), where f and g are twice differen- tiable functions, show that d'y _ dy…

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Q: given y = ƒ(u) and u = g(x), find dy/dx =dy/dx = ƒ'(g(x))g'(x). y = -sec u, u = 1/x+ 7x

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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: Suppose that u and v are differentiable at x = 2 and that u(2) = 4, v(2) = -9, u'(2) = 5, and v'(2)…

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Q: • If u = x+ 1 t=yu y t then, %3D 1. dy =D0 dx dy dx dy = 1 2. 3.

A: The given functions are u=x+1, t=u  and y=t2. Convert the function y in terms of x as follows.…

Q: Use logarithmic differentiation to prove that

A: We have to prove that ddxuxvx=uxvxdvdxlnux+vxuxdudx Assuming, y=uxvx Taking logarithm both sides,…

Q: 2. Show that the function u = p(xy) + VTÝ v(y/x) provides the equation „Pu dx² 0. dy²

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Q: Evaluate dx f(t) dt and * f(t) dt, where a and b are constants.

A: To evaluate: ddx∫axft dt and ddx∫abft dt, where a and b are constants. Solution: The fundamental…

Q: • If u = x+1 t= yu y= -t² then, %3D dx dy 2. = X dx dy 3. dx %3D dy 4. :-1 dx I||| 1.

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Q: (a) If ƒ and g are differentiable functions, then dx dy (b) If y = csc¬1 u and u is a function of x,…

A: a) if f and g are differentiable function then df(x)dg(x) = f'(x)g(x)-f(x)g'(x)g2(x)

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: fyx if f(x, y) = sin(xy) + x² In y

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Q: +! dy dx x dx A- If Z = d'y x dx x dx? Prove that Z.Z = xp -1% NI X

A: A Given Z=d2ydx2+1xdydx. We need to evaluate Z.Z. Consider Z.Z.…

Q: d y is a differentiable function of x . Write dx dy in terms of x , Y , and dx

A: Dear students as per our rule, in one session we can only solve one question. Please post the other…

Q: d dx y' z' y" z"

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Q: Suppose u and v are functions of x that are differentiable at x = 0 and that u(0) = 2, u'(0) = - 8,…

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Q: Provide an appropriate response. Suppose that y is a function of u, and that u is itself a function…

A: y is a function of u, and that u is itself a function of x. How does one find the derivative of y in…

Q: S dy S f(x, y)dx

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Q: Suppose u and v are functions of x that are differentiable at x = C and that u(0) = 1, u'(0) = 7,…

A: Solve the differentiation

Q: Let y be a function of x and suppose x*-y+xy=5_what is the correct result for the derivative of y…

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Q: Evaluate //| (x + y – 2z) dV where E = {(x, y, z) | - 2 < y < 0,0 < x < y, 0 < z < x + y²}

A: A detailed solution is given below.

Q: (e) 3x E R, Vy E R, xy > 0. (f) Vx E R, 3y E R, xy > 0. (g) 3x E R, Vy E R, xy > 0.

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Q: given y = ƒ(u) and u = g(x), find dy/dx =dy/dx = ƒ'(g(x))g'(x). y = cos u, u = e-x

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Q: Suppose u and v are differentiable functions of x and that u(0) = 5, u′(0) = -3, v(0) = -1, v′(0) =…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Suppose u and v are functions of x that are differentiable at x = 0 and that u(0) = 5, u'(0) = -3,…

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

A: To find

Q: Let f (x, y) = csc(x + y³) ey , find дудх

A: The given function is  f(x,y)=csc(x+y3)exy. The main objective is to evaluate ∂2f∂y∂x.

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: Suppose u and y are differentiable functions of x and that u(1) = 2, u′(1) = 0, y(1) = 5, y′(1) =…

A: We will Use the following rules.Chain Rule:Suppose that we have two functions f(x) and g(x) and they…

Q: dy (a) Find if y = (In x)=². dx

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

Q: Evaluate ff, xy.cos yz dx. dy. dz D = { (x,y, z): 0 <xS1 & 0<ysl & 5:50

A: We have to evaluate ∭Dxy⋅cosyzdxdydz, where D=x,y,z:0≤x≤1 and 0≤y≤1 and 0≤z≤π2 Now,…

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: √√√(-) True f(x,y) dx dy False - L.T. 1.². f(x, y) dy dr

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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: given y = ƒ(u) and u = g(x), find dy/dx =dy/dx = ƒ'(g(x))g'(x). y = sin u, u = x - cos x

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Q: Suppose y is a function of x. Which of the following is d(x^3y) dx ? * 3x^2y + x^3dy dx 3x^2y 2x^3dy…

A: Givendx3ydx

Q: Let y be a function of x and suppose y=In(x²+ y²). What is the correct result for the derivative of…

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Q: Let y be a function of x and suppose y = In(x²+y²).What is the correct result for the derivative of…

A: Given y=ln(x2+y2)

Q: Given y=h(x).p(x),where h(x) and p(x) are differentiable function of x,show that dy/dx…

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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 = ?