Find dy/dx if y = x3/2 by using the Chain Rule with y as a compositionof y = u3 and u = √x

Q: Find the first partial derivatives for f(x,y)= 9x cos (3xy). of dx

A: To find the first partial derivatives  f(x,y) =9x cos 3xy

Q: (a) By using thẻ chain rülé and the dérivative (1, (1xl) = {"1, if x>0 if x<0' d %3D dx 1-1, find -…

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Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: Given y=e5x-7 Let u=5x-7, then y=eu dydu=eu and dudx=5 Version 1 of chain rule is given by…

Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: y=5x2+11x20Chain rule:dydx=dydu.dudx

Q: If y = 2x^2 - 3x and dy/dt = 3, find dx/dt when x=2.

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Q: Find dy/dx if y = x3/2 by using the Chain Rule with y as a compositionof y = √u and u = x3

A: Recall the chain rule of differentiation:

Q: Use Version 1 of the Chain Rule to Calculate dy/dx

A: To calculate the derivative of the given function using chain rule: y=3x2+7x10

Q: Compute dy and Ay for y =-4x – 3 at x = -1 with Ar = dx= -0.06. Give your answers to four decimal…

A: Given data: fx=y=-4x2-3, x=-1 and ∆x=dx=-0.06 We know that ∆y=fx+∆x-fx Substitute the values in…

Q: dx =- 1. dt dy at x = 2 if y = 4x° – 2 and dt %3D Find - dy dt

A: Given: y=4x2-2 and dxdt=-1 To find: dydt, when x=2.

Q: Find the requested partial derivative. dz 3 if z° = z+ xy - 1 and y = x+ y- 1 dy 3

A: We have to find partial derivative

Q: Find the second order partial derivatives and of дхду aydx S(x.y) = 4x + In x + e² cos y + 9y + 3

A: d/dx(x^n)=nx^n-1 d/dx(cosx)=-sinx

Q: Find dy/dt if y=ln(t^2+1)/(squareroot of (4-t)

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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: 3. Find the partial derivatives du and ou if uw = x sin (y), x = s² +t? and y =;,

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Q: Let y=5x2y=5x2.Find the change in y, Δy when x=3 and Δx=0.2   Find the differential dy when x=3 and…

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Q: Differentiate implicitly to find the first partial derivatives of z…

A: the given implicit function is:xlny+y2z+z2=8

Q: If f(x, y) = 3x² – 7y, then the total differential of ƒ at x = 1 and y = -2 is :

A: we need to find the total differential of the function  f(x,y) = 3x2 - 7y2 the total differential,…

Q: Find the differential dy. x + 3 4x - 1 dy =

A: y=x+34x-1

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: Q4) Use the chain rule to express dy /dx in terms of x and y t2 y = t2+1 and t = 3x3 – 3 where x =1

A: Given y=t2t2+1 and t=3x3-3 and x=1

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: Compute the differential dz of the function. z = x'y8 dz

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Q: 94. Find dy/dx if y - 2 by using the Chain Rule with y as a com- position of a. y- u' and - V b. y -…

A: a) Given y=x32 The chain rule state that dydx=dydu·dudx

Q: Find the first partial derivatives for f(x.y)= 10x cos (3xy)

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Q: Find the Wronskian for the differential equatio: dy dx2 fip dx 3 10y = 0

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Q: Find dy/dx by using Leibniz’s notation for the chain rule: dy/dx = (dy/du) (du/dx) y = (tan x + sin…

A: The given function is y=tanx+sinx-3 We have to find dydx by using Leibniz’s notation for the chain…

Q: Use chain rule to find dy/dx for y=u^4/3 , u=x^2+8x+30

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Q: Differentiate the function y = 6 + x using the Chain Rule. dy %3D

A: Given, the function is                              We have to differentiate this function using…

Q: If f(x, y) = y cos(x) – x³ In(y), find the second partial derivative dy dx

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Q: Find the first partial derivatives for f(x,y) = x cos (5xy). of = cos (5xy) - 5xy sin (5xy) %3D of…

A: The solution for the above question is as shown below.

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

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Q: t seel dx

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Q: Find the partial derivative with respect to x of e^y-2*ln(x)-x^3y^2.

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Q: Suppose 4x + 9y - 25, where x and y are functions of t. (a) If dy/dt-, find dx/dt when x = 2 and y =…

A: Given: 4x2+9y2=25 Since, x and y are functions of t, therefore differentiating each sides with…

Q: Q3) Find dy/dx if 1- y= In /x 2- y3xsin

A: 1) d(ln(x))dxApply the chain rule: 12ln(x)d(ln(x))dx

Q: If z-f (x y): then its total differential can be expressed as * (),中 (). dyds dy + dz O Option 2 O…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = xV9 - x2

A: Use  the differential of the form f = u.v

Q: If z = sin(x/y) and x = ln (u) and y = v^4, find the partial derivatives of z with respect to u and…

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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: 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: 3. Find dy, where; (x+y) = 2 a) cos (xy)- + e b) e+ iPtany=1 , u= xlax (use chain rule)

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Q: Find dy/dx by differentiating xe²y + 7 = 4y² – 5ª implicitly.

A: Given: xe2y+7=4y2-5xDifferentiate both side with respect to x

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: Find dy/dx by using Leibniz’s notation for the chain rule: dy/dx = (dy/du) (du/dx)  y = (2 x3 − x2…

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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: Find the integrating factor of (x² - y²)dx + (x² - 2xy)dy = 0

A: Given  (x2-y2)dx+(x2-2xy)dy=0

Q: Find dy/dx by the implicet differentiasion x2+y2=64

A: