a) by using the chain rule and (b) by converting w to a function of t before differentiating w= ln(x2+y) , x= 2t , y= 4-t

Q: Eliminate the arbitrary constants (a, b) in the function to obtain the differentialequation. I e =…

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Q: Find the second partial derivative for the function z = x7-7xy + 6y2 with respect to x.

A: Solution of given question is written in below steps.

Q: Let y = 2x2. Find the change in y, Ay when x = 5 and Ax 0.1 Find the differential dy when x = 5 and…

A: We have to solve

Q: The relative displacement u(t) of a single-storey shear building subjected to an earthquake ground…

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Q: Find the differential dy of the given function.     y = 3x2/3

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Q: Find the second-order partial derivatives of the given function, and verify your answer using…

A: The given function is fx, y=y2-3xy+cosy+7ey. The second order partial derivatives of the given…

Q: Let y = 4x2 + 4x + 3. Find the differential dy when x = 1 and dx 0.4 %3D Find the differential dy…

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Q: If x2 + y2 = 25 and dx/dt = -2, then what is dy/dt when x = 3and y = -4?

A: Given x2+y2=25Differentiating with respect to t,ddtx2+y2=ddt25

Q: Q1-Use the chain rule to express dy / dx in terms of xand y: 1-1 a) y = аnd x = at 1= 2 1+1 b) y=1-…

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 3x2 - 5 dy =

A: Given, y = 3x2-5  We have to find the differential dy for the given function

Q: 2. Let f(x, y,2) = z-sin(xy), x = t, y = In t, z = e. Find derivative of f directly and by using…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = In (√9-x²) dy =

A: Given: y=ln9-x2 To find the differential dy

Q: Find ôw/ðs and aw/dt using the appropriate Chain Rule. Function Values w = y3 - 2x2y x = e, y = e s…

A: Given query is to find the partial derivatives.

Q: Find the differential dy of the given function. y = 3x2 − 4

A: Given function is Differentiating with respect to x, we get Therefore , differential dy is

Q: Find the differential dy of the given function. y = InV9 - x2 dy =

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Q: Transforming A S B © D dx secx + 1 7 dz 1-2² 1==323d² -dz 1+z² [1+2²21 2-272 1+z² -dz -dz using…

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Q: For the differential equation: dy/dx = 2x + y, compute dy/dx for x = -2, -1,0,1,2, y = -1,0,1 and…

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Q: 4. Given y = 3u² – u and u = x³ – 1, use the Chain Rule in Leibniz notation to find the value of dy…

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Q: Find the total differential. w = e3y cos(5x) + z5 ||

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Q: 1. Find the total differential dw. 2. w = re2u +e-V

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Q: A particle moves on the graph of y^2 = x + 1 so that dx/dt = 4x +4. What is dy/dt when x =8 ?

A: We have, a particle moves on the graph of a function given as y2=x+1 Differentiating both of the…

Q: Let y = 4x“. Find the change in y, Ay when x = 3 and Ax Find the differential dy when x = 3 and dæ =…

A: Given that: y=4x2, x=3 and ∆x=0.4

Q: Show that the function y =  A e-x    + B x e-x satisfies the differentialequation y"   +2y' + y  =0

A: The given differential equation is y''+2y'+y=0. Let y=Ae-x+Bxe-x. This implies that,…

Q: S(«,9) =7+3y Also, find the total differential of the function.

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Q: Find the differential dz of the function f(x,y)=4y2+x2y−2xy and use it to approximate Δz at point…

A: Find the differential dz of the function f(x,y)=4y2+x2y−2xy and use it to approximate Δz at point…

Q: Find aw/as and dw/at using the appropriate Chain Rule. Function Values w = y - 9x3y x = e, y = ef s=…

A: Partial Derivative of Chain Rules

Q: For the function f (x,y,z,w) with x, y, z, and w all functions of s, t, andr, write out the chain…

A: The function is fx,y,z,w x,y,z,w are functions of s,t,r.   Partial derivative of a function with…

Q: Given the Ideal Gas Law: P = 10T/V where P is pressure, V is volume, and T is temperature. Find the…

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Q: Let y = 3x² + 8x + 3. Find the differential dy when x = Find the differential dy when x = 2 and da 2…

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Q: If f(x, y) = y² cos(x) – x³ In(y), find the second partial derivative ду дх

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Q: 4. Given that c(t) = t² + 2, y(t) = t³ – 2t and f(x,y) = x² sin (xy). Using the df and evaluate it…

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Q: Find the differential dy for y = x2 - 4x + 6, then evaluate it when x = 2 and dx = 0.1

A: Differentiate the given curve y=x2-4x+6 w.r.t.  x use the power rule of differentiation i.e.…

Q: The time rate of change of liquid circulating in two tanks is govemed by dy -0.02x + 0.02y, = 0.02x…

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Q: Consider the nonhomogeneous differential equa 1 "(x) + y(x) = e '+ sin a

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Q: given that, x(t) =t2 +2    ,y(t)=t3 -2t  and f(x,y) =x2 sin(xy) . using the chain rule for partial…

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Q: A point is moving along the graph of the function y=1/8x^2 +3 such that dx/dt = 3 cm/sec. Find dy/dt…

A: NOTE: Refresh your page if you can't see any equations. . take the derivative with respect to t

Q: Let y=3x^2  Find the change in y, Δy when x=5 and Δx=0.1    Find the differential dy when x=5 and…

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Q: Let x and y be differential function of t and suppose they are related by the equatin xy-1=y^2. Find…

A: Differentiating with respect to t, we get

Q: Consider the functions z=2e* In y, x= In (u cos v), and y = u sin v. dz dz (a) Express and du as…

A: Given: The functions, z=2exlny, x=lnu cos v, and y=u sin v.

Q: The dynamics of a fish population is described by the Richard's growth law dN (1) dt where N = N(t)…

A: rN is the part of the equation which signifies the rate of change of population dN/dt. r is the…

Q: Find the differential dy of the given function. Xx + 5 y = 2х — 9

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Q: 10. Use the Chain Rule to find the indicated partial derivative if ax F = Vu? + v2 + w², u = xe, v =…

A: F=u2+v2+w2To find ∂F∂x

Q: Consider the functions z = 2 e In y, x = In (u cos v), and y = u sin v. dz ze as functions of u and…

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Q: Let y = 2x². Find the change in y, Ay when x = 4 and Ax = 0.2 Find the differential dy when x = 4…

A: It is provided that y=2x2. We need to determine ∆y for x=4, ∆x=0.2 and We need to determine dy for…

Q: Let y = 3x² + 8x + 3. Find the differential dy when x = 1 and dx = 0.2 Find the differential dy when…

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Q: Let y=(x2+4)to the 4th power. Find the differential dy when x=3 and dx=0.3.... Find the…

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Q: dw 3. Given w=ln (x²+y) where x=2t , and y=4-t . Find in two ways: dt (a) Using the appropriate…

A: Given:- w = ln(x ^ 2 + y) where x = 2t , and y = 4 - t . To find:- dw/dt (a) Using the appropriate…