Let f (x,y) = 3x e with x(t) = 9 e and y(t) = t. Find the derivative of w f(x,y) with respect to t when t=D 0. ..... dw When t = 0, then dt

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

A: topic - derivative of a function

Q: Can you help me with this problem step by step?

A: The given equation,

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

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

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

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Q: Let y = f(x), where f(x) = 5x² + 5. Find the differential of the function. dy = X

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Q: Let y = f(x), where f(x) = Vx + 4. Find the differential of the function. dy =

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Q: Let y = tan find the differential dy of the function.

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Q: Use the Chain Rule to find the derivative of w = xy with respect to t along the path x = cos t, y =…

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Q: Find the derivative of y with respect to t. 3. 0<t< 2 y = sec 2t3 dy dt

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Q: Find the derivatives of y with respect to x: a) y = xe* – ex b)' y = e(+x+) c) y = e*(sin x + cos x)…

A: Differentiate the function with respect to x.

Q: Find the derivative of y with respect to t. y = t(In 11t)? dy %3D dt

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Q: Find the value of the derivative of ƒ(x, y, z) = xy + yz + xz with respect to t on the curve x = cos…

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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: Find the derivative of y with respect to x. y = 9 In (6 In x) dy %3D dx

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Q: Find the derivative of y with respect to t. y = csc -1(e') dy dt

A: The chain rule of derivative states: f∘g'=f'(g)×g'. The derivative of exponential function is…

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

A: Proceed as shown below....

Q: The current in a wire is defined as the derivative of thecharge: I(t)  =Q'(t). What does  ∫ab I(t)…

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Q: Why does this work? If we have the curve in the xy-plane: F (x, y) = 0, then why is the implicit…

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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: Find the derivative of y = 7 In(sin t + 5). dy/dt =

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Q: If f(x,y) = ln(xy) + x2y2, in what directions is the second directional derivative of f(1,1) = 3?

A: Given function fx,y=lnxy+x2y2 Consider unit vector u⏞=12,32  Now, Du⏞f=∇f·u⏞             ∇f=fx,fy…

Q: Let y = f(x), where %3D 7 f(x) = x + Find the differential of the function. dy =

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Q: Find the derivative of y with respect to t. y=e(cos t+ln t) dy/dt=???

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Q: Find the derivative of the y with respect to t. Y=ln(t^2) dy/dt

A: To find the derivative of Y=ln(t^2) with respect to t.

Q: let f(x,y)= z-sin(xy),x= t, y= lnt, z=e^t-1. find derivative of f directly and by using chain rule…

A: Plug the given expressions of x,y, and z. Then differentiate directly. And plug t=1

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

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Q: Find the derivative of the function. s = t In |t| ds dt 11

A: The objective is to find the derivative.

Q: Find the derivative of y with respect to t. 1 y = sec 1 0<t< 5t4 dy dt

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

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Q: find the derivative of y with respect to x, t, or u,as appropriate. y = e^(cos t + ln t)           .…

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: H.W: Use the chain rule to find the derivative of w= x² + y² with respect to t dw dt with x = cost +…

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

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Q: H.W: Use the chain rule to find the derivative === with x = cos² t, y = sin² t, z = - at t = 3 dw xy…

A: Solution :

Q: Find the derivative of y with respect to t y = In (t2) dy %3D dt

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Q: Find the derivative of y with respect to t. y3 t(ln 10t)2 dy dt

A: we have to find derivative

Q: b) Find the value of the derivative of f(x, y, z) = xy + yz + xz with respect to t on the curve x =…

A: There are two methods to do this: One is direct method which we used and other is by chain rule.

Q: H.W: Use the chain rule to find the derivative of w=x² + y² with dw with x cost+ sin t, y= cost-sint…

A: If w is a function of x and y and x,y are functions of t then we get by Chain rule, dw/dt=…

Q: Suppose that y is a differentiable function of x and w = cos(y5). Express the derivative of w with…

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Q: x and y are functions of a variable t and use implicit differentiation to relate dy/dt and dx/dt.

A: Differentiate both sides with respect to t And use the product rule

Q: Find the value of the derivative of g (x, y) when we restrict to the curve defined by x = cos t and…

A: Differrtiate with respect to t

Q: Find the derivative, dy/dx of the following using the chain rule: a) y = 3. 'x+1 b) y = ()³ 5x+1 %3D…

A: As per guidelines we can solve only one question at a time so if you need more answers kindly repost…

Q: Find the derivative of y with respect to t Y= ln (t^11) dy/dt=

A: If y=f(t)=ln(t) then  dy/dt = f'(t) = 1/t.

Q: Let f(x,y) = 8x + 10y with x(t) = cos t, and y(t) = sin t. Find the derivative of w = f(x,y) with…

A: Here we have to find the derivative of w with respect to t.

Q: Find the derivative of y with respect to T Y=t(ln 4t)^2 dy/dt

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Q: Find the derivative of y with respect to x. y = (x° In x)3 dy %3D dx

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Q: H.W: Use the chain rule to find the derivative of w = x² + y² with dw respect to t dt with x = cos1…

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Q: Find the derivative of y with respect to v. y=v1-v2 +5 cos - 1, y = dy dv II

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