Both x and y denotefunctions of t that are related by the given equation. Use this equation and the given derivative information to find the specified derivative. Equation: x + 7y = | dx la) Given that = 3, find - dt dy when x = 4. dt Enter the exact answer. dy dt dy = 8, find dt dx when x = 5. dt (b) Given that dx dt

Q: Find the 2nd and 3rd derivative of the function y'= 3x^2y^2 with respect to dy/dx

A: Find the 2nd and 3rd derivative of the function y'=3x2y2with respect to x

Q: 9 tan t Find the derivative of the function y = 2 + 2 sect dy dt

A: Explanation and solutions is given below....

Q: Find the second derivative d2y/dx2 of the implicit curve y3=xy+1  at (0,1)

A: y3 = xy +1differentiating both wrt to x3y2dydx= y+xdydx+0dydx3y2=ydydx= y3y2-x

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: find dy/dx of each equation using implicit differentiation. a. y4 -2y2x2 + 3x2 = 0 b. (x + y)3 =…

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Q: 1.x3 = at?, find the second derivative of "x" with ,d²x respect to "t", 'dt2

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Q: Find the derivative of y with respect to s. y%3Dsec -1 (2s4 + 7) dy ds

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Q: Can you help me step by step?

A: Let y = f(u) then solves the derivative by applying the chain rule:

Q: ind dy/dx using the rules for finding derivatives: (a) y = (6x^2-8)(3x^2-9

A: The given function is  y=6x2-8 3x2-9x+3 To find the derivative of the give function ,  y=6x2-8…

Q: Both xand y denote functions of t that are related by the given equation. Use this equation and the…

A: difrentiate equation with respect to t and plug all the information.

Q: Find the directions in which the function f(x, y) = x²y+exy sin(y) Increase and decrease most…

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Q: Given that y is a function of x defined implicitly by the equation: siny = 4x + xy dy Find the first…

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Q: Both x and y denote functions of t that are related by the given equation. Use this equation and the…

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Q: Can you help me step by step?

A: To differnetiate the given function y(t)

Q: dw H.W: Use the chain rule to find the derivative dt with x = cos x = cos² t, y = sin² == and…

A: Given :w=xz+yzx=cos2t    and y=sin2t   z=1t

Q: Given the equation z=f(x, y) = ln(x² + 2y² +1) with the change of variables x=3-1² and y = 4t-1³,…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the derivative. y = 3t cos (t6) dt Select one: 3 A.6x cos (x ) 3 3 B.3 cos (x ) - 3^/x sin (x )…

A: The solution are next step

Q: Both xand y denote functions of t that are related by the given equation. Use this equation and the…

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Q: Use the appropriate form of the chain rule to find the derivatives. w = 12x2 + 12y² + z²; x= p sin o…

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Q: Both x and ydenote functions of t that are related by the given equation. Use this equation and the…

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Q: Use the appropriate form of the chain rule to find the derivatives. 12x2 + 12y2 + z²; x = p sin o…

A: Given:  w = 12x2+12y2+z2 x=ρ sinϕ cosθ, y=ρ sinϕ sin θ, z= ρ cosϕ  Find: ∂w∂ρ, ∂w∂ϕ and ∂w∂θ Chain…

Q: Derive the formula dy 1 dx 1 + x? for the derivative of y = tanx by differentiating both sides of…

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Q: A particle, initially at rest, moves along the x-axis such that its acceleration at time t > 0 is…

A: Given acceleration, a(t)=cost,       t>0 And v(0)=0, x(0)=3

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

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Q: A particle moves in a straight line and any time t seconds, its velocity v m/s is given dx by e-".…

A: Note that velocity is rate of change of displacement. Hence displacement will be integration of…

Q: Find the derivative of y=2ecos.x)(sin(5x)) d'y Calculate as a function of t if x=t-t and y=t-t 2 dx?…

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

A: Given :y=cos4xdxdt=-3 when x=π8 Use chain rule to evaluate the dydt. According to chain rule,…

Q: Assume that x and y are both differentiable functions of t and find the required variables below.…

A: x and y are both differentiable functions of t y=x We need to find implicit differentiation dydt a)…

Q: Find the derivative of y with respect to t. y = t(In 1t)2

A: The given function,  y=t ln 1t2

Q: Find the derivative of y with respect to s. y = sec 1 (5s° + 2) dy ds

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Q: Given the equation X^3+ Y^3 =28x Find the dy over dx using implicit differentiation

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Q: "Differentiate both sides of the equation V = Tr*with respect to t AP (using the chain rule on the…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = -2x - (sin(x))² dy= Need…

A: Using derivative

Q: 1. 2x'y² + 4yx² = 6. Find dy/dx at (1, 1) by i- %3D

A: Here we have, 2x3y2+4yx2=6 ................... (1)  Differentiate with respect to x

Q: Both x and y denote functions of t that are related by the given equation. Use this equation and the…

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

A: To find the derivative of the given function. And , find the value of constant in the equation.

Q: Find the derivative. d | dx + 0 OA. x³ sin (x¹) +5, ○ B. sint dt C. 4x³ sin (x4) - cos (x4) - 1 D.…

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Q: If z = xy and x = e=' and y = sin(t), find the following derivative using the chain rule. Enter your…

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Q: Find the differential dy of the given function. y = csc 3x Jax dy Need Help? Read It

A: dy = ? dx

Q: Both x and ydenote functions of i that are related by the given equation. Use this equation and the…

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Q: dw of w: dt x y Use the chain rule to find the derivative 1 with x cos t, y = sin t, z =- dw and…

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Q: Calculate the derivative of the following function. y= cos (8t+ 15) dy dt

A: Differentiation of cos that ha is -sin thehtha. We will use changing rule to find dy/dt

Q: Find the derivative of the function. y = (3t – 1)(6t – 6) -1 dy dt II

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Q: 2. In each case, find the derivative d. (a) z = x³ – y² and x(t) = cos 2t and y(t) = e-3t, (b) z =…

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Q: Can you help me step by step?

A: We use chain rule of differentiation which states that if f(x)=g(h(x)), then f'(x)=g'(h(x))h'(x)

Q: 1. Find the derivative of the following functions (dy/dx) at x=0 y= sin 2x – 2sec x 2. Find the…

A: We are given: y=sin 2x - 2 sec x and y = sin4 4x - cos4 4x We need to find their derivatives at…

Q: Find the indicated derivative: d/dt ( (t^3 +3, 3t^2 -4)* (tan(t),sin(t)) )

A: We have to Find the derivative of d/dt ( (t^3 +3, 3t^2 -4)* (tan(t),sin(t)) )

Q: dw of w==+ dt x. y Use the chain rule to find the derivative with x = cos 1, y = sin ?t, z = - dw…

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Q: Suppose that x² + y² = 82. dy (1) Use the method of implicit differentiation to find dx dy dx (2)…

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Q: Use the chain rule to find the derivative of the function z = 2a*y³ – xy? along the curve given by x…

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