dz If z = e2x+ 3y and x = In t, y = t2, calculate from the total dt derivative formula and show that it agrees with the result obtained by substitution for x and y before differentiating.

Q: 1. Suppose y = f(x) and that x is changing over time. How is dy/dt related to dx/dt?

A: Given that: y=f(x)

Q: Give xy+x^2 y=2 such that dx/dt=2 in/sec. FInd dy/dt for x=1

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Q: hi, i've added the problem as a picture please take a look. thanks in advance!

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Q: If z = (x +y) eª and ¤ 3t and y = 1 – ť², find the following derivative using the chain rule. Enter…

A: See the attachment

Q: 4. Use the chain rule to find out the total derivative dv/dt, when v = xe/z, where r = t²,y = cos t,…

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Q: Find dw/ds and dw/at using the appropriate Chain Rule. Function Values w = sin(4x + 5y) X = s + t, y…

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Q: (b) If z= 3x² + y² 4xy Hence, Show that find ôz dz dx dy Ox 3 3x a²z y a²z y ổr x ô and =0 8² z 2…

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Q: suppose that x and y are both differentiable functions of t and are related by the given equation.…

A: Given:        x2+2xy=y3

Q: y, thên thế total differential of and y O df = 11 dr + 16 dy O df = 15 dr + 19 dy O df = 12 dr +18…

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Q: Take a look at the derivative of the integral (4t² – 2t + 7) dt. d - dx -4

A: topic - derivative and integration

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Given Equation: and given that dx/dt = 3 Find  (a) dy/dt when x = 4,…

Q: suppose y = √(3x + 1), where x and y are both functions of t. If dx/dt = 2, find dy/dt when x=5

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Q: Assume that x=x(t) and y=y(t). Let y=x^2+2 and dx/dt=2 when x=5. Find dy/dt when x=5

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Q: Find the derivative d dy dy (3y?) = ay + by +c- dt dt dt

A: Proceed as shown below....

Q: Suppose that a = x(t) and y = y(t) are both functions of t. If y + xy – 3x = 23, and dy/dt = 1 when…

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Q: Suppose that x=x(t) and y=y(t) are both functions of t. If x2 + y2 =17, and dx/dt=2 when x=4 and…

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Q: suppose that x and y are both differentiable functions of t and are related by the given equation.…

A: x2y2=2y3+1

Q: Q1J Use the Chain rule to find the derivative of w=xy + In z with re spect to v if x v/u, y u+v, z…

A: The chain rule is used to calculate the derivatives of the function. The chain rule for a function…

Q: w =sec (xyz) - Yx +y+z

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Q: Find dw/ds and aw/at using the appropriate Chain Rule. Function Point w = sin(5x + 6y) X = s + t, y…

A: According to guidelines we solve only first three parts.

Q: If f(x, y) = y cos(x) – x* In(y), find the second partial derivative (A dx? -y? cos(x) – 6x In(y) d…

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Q: Assume that x = x(t) and y = y = y(t). Let y=x^2+4 and dx/dt =2 when x=5. Find dy/dt when x=5

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Q: Find ðw/ds and dw/at using the appropriate Chain Rule. Function Values w = sin(4x + 5y) x = s +t, y…

A: We will find out the required value.

Q: Find the derivative of the function. s=t° In t| ds dt

A: The solution is given below in the next step:

Q: Find the total derivative of the function f(x, y, z) =+z In (2x+1)+sin (xy) xz

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Q: Suppose that x=x(t) and y=y(t) are both functions of t. If y=2x2−1, and dx/dt=5 when x=14, what is…

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Q: If x = y3 - y and dy/dt = 5, then what is dx/dt when y = 2?

A: Given,

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: To find the antiderivative of the below derivative

Q: If L = 2x2 + y2, dx/dt = -1, and dy/dt = 3, find dL/dt when x = 5 and y = 1

A: Consider the provided equation and information,

Q: 4. Given xy+x*y=2 such that d/dt =2 in/sec. Find dy/dt for x= 1

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Q: suppose that x and y are both differentiable functions of t and are related by the given equation.…

A: Suppose that x and y are both differentiable functions of t and are related by the given equation…

Q: Find the total derivative dz/dt , given z = x2-8xy-y3 , where x= 3t and y= 1–t

A: Suppose z is a function of x and y that is z=fx,y where x and y is the function of t that is x=xt…

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Given : Equation x2 + y2 = 25 and x and y both differentiable functions of t.   To find : (a)…

Q: Find the total differential. z = 5x3y8 dz =

A: The solution is:

Q: Assume that x and y are differentiable functions of t. Find  dx/dt given that x= -3 , y= -2 , and…

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Q: Find dy/dt when x=4 and dx/dt=-3, given that x^3+y^3=72

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Q: Suppose that r = x(t) and y = y(t) are both functions of t. If %3D y = 2x/2 + 3, and dx/dt = 5 when…

A: The given function is: y=2x12+3

Q: Given xy+x 2y =2 such that dx/dt = 2in/sec. Find dy/dt for x=1.

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Q: Use the method of first principles to show that d/dt(lnt)=1/t

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Q: Find the indicated derivative. dy dt - for y = (2.2t - 4t?)(2t + 1.9) dt 11

A: We have to find dy/dt for Given function.

Q: Find dy/dt using the given values. y = x3 - 5x for x = 3, dx/dt = 4. dy dt

A: Value of dy/dt= 88 See the calculation below

Q: Find dw/ds and dw/at using the appropriate Chain Rule. Function Values w = sin(4x + 5y) x = s + t, y…

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Q: Assume that x=x(t) and y=y(t). Let y=x2+3 and dx/dt=4 when x=5.Find dy/dt when x=5.

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Q: Find ôw/as and ôw/at using the appropriate Chain Rule. Function Values w = sin(7x + 8y) x = s + t, y…

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Q: If y = x2 and dx/dt = 3, then what is dy/dt when x = -1?

A: Differentiate both sides with respect to t.

Q: Find the total differential. z = 6x *y5 iz

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Q: Suppose both x and y are functions of time (t). Find the rate of change of y with respect to t, that…

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Q: If xy + z² = z, and dx/dt = -1, dz/dt = 3, find dy/dt when x = 2 and z = 4

A: Given: xy+z2=z and dxdt=-1, dzdt=3  Find dydt when x=2 and z=4 differentiate  xy+z2=z with respect…

Q: If z = e2x+ 3y and x = In t, y = t2, calculate dz from the total dt derivative formula and show that…

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Q: If x^2+y^2=25 and dx/dt=6, find dy/dt when y is positive and (a) x=0: x=1 x=4

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