Q1/ Use the chain rule to find and when z = tan- (=) X = u cos V, du dv y = u sin v at point (u, v)=(1.3, a/6).

Q: y(x) = tan{/3x² + In(5x*) - In(5x'

A: Given  y(x) = tan3x23 + ln5x4 We have to find dydx.

Q: y=8sin(x)cos(x) ; x=pi/3

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Q: Compute the indicated derivative using the chain rule. dy x = 4 + 3t, y = -7t; dx dy dx ||

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Q: Use the appropriate form of the chain rule to find the derivatives. w = 3x? + 3y? + z²; x = p sin $…

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Q: Compute the indicated derivative using the chain rule. x = 6 + 3t, y = −8t;  dy dx

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Q: Compute the indicated derivative using the chain rule. dy x = 1 – t/3, y = 8t – 1; dy %3D

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Q: Find the first derivative: y = In sin e Oy = 2e sece Oy = -2e cot e= Oy = 2e tane Oy = 2e cscez

A: Solve by derivation

Q: What is the average rate of change of y = cos (2x) on the interval [0,π/2]

A: Given f(x)= y=cos (2x) to find the average rate of change over the interval (0,pi/2) average rate of…

Q: dx/dt of -ln(-cos t)-e^(sin t)

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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: use the chain rule to find: 28) dv 2- COSxy + y cos x

A: Solution:Given   z= cos xy+ y cos xx=u2+v and y=u-v2To find :dzdvFormula:ddx(cos x)=-sin…

Q: Compute the indicated derivative using the chain rule. dy x = 5 + 3t, y = -8t; dx dy %3D dx

A: We have to find the indicated derivative by using chain rule: x=5+3t, y=-8t Differentiating first…

Q: If sin(5x - 5y + z) = 0, use implicit differentiation to find the first partial derivatives with…

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Q: Find the linear approximation of the function at the given point. f(x, y) = 4 sinx - 6 cos y at (0,-

A: Given,           The function fx,y=4sinx-6cosy  at  0,π2.

Q: b) Find if Scosy Vt3 + 5 dt + tany = x -sinx b) Find if S* Vt2 + 5 dt + siny = x – x°cosy dx2

A: Solve by differentiation

Q: Let y tan(4x + 6). Find the differential dy when x = 5 and dx = 0.2 Find the differential dy when x…

A: Given : y = tan(4x + 6)   To find the differential dy when x = 5 and dx = 0.2 Also to find the…

Q: Integrate: | cos" z dx

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Q: Find partial derivative of dx for the function f(x.y) given below exp 2x. siny .(at the point (In2,…

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

A: We differentiate the function with respect to t.

Q: Let y = tan(5x + 2). Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

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Q: . z=tan 2x dx From their derivatives find

A: Question is solved.

Q: in integrating the function fx cos() dx using intogration by parts, whut would you choose for your…

A: Solution

Q: Find Partial Derivatives for z = sin(x)cos(xy)

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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: Let y tan(5 7) Find the differential dy when x = 3 and da 0.4 Preview 3 and da 0.8 Find the…

A: Given function:

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: If Z = Jxy +y, x= cos 0 , y= sin 0 when 0 dz By using chain rule find de

A: Chain rule for one independent variable- Suppose that x = g(t) and y = h(t) are differentiable…

Q: 5. Use Implicit differentiation to find dy when y V x2 tya = 15x° +4siny 3

A: Using implicit differentiation find dydx for;  yx2+y2=15x3+4siny

Q: Let y tan(4x + 3). Find the differential dy when z = 3 and dx = 0.1 Find the differential dy when r…

A: y=tan4x+3

Q: Let y = tan(4x + 7). Find the differential dy when x = 2 and dx = 0.3 Find the differential dy when…

A: Since you are asking multiple questions. We are answering only the first question as per our…

Q: Compute the indicated derivative using the chain rule. dy x = 1 - t/3, y = 8t – 1;- dx dy dx

A: x=1-t3 differentiating with respective t dxdt=-13 y=8t-1 differentiating with respective t dydt=8

Q: Find the first-order partial derivative with respect to x of f(x,y) = e5x siny.

A: To find the first-order partial derivative with respect to x, given function, fx,y=e5x sin y

Q: B: Use the Chain Rule to find the derivative of f(x,y) xy with respect to (t) along the path y =…

A: Solution:-

Q: Let y = tan(2x +5). Find the differential dy when x 3 and dr = 0.1 Find the differential dy when z =…

A: Given that y=tan(2x+5) find the differential dy when x=3 and dx=0.1 find the differential dy when…

Q: ey sin x = x + xY %3D

A: Solution:- The given implicit function is  ey sinx=x+xy

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

A: The given function,w=sin(4x+5y)x=s+ty=s-tat the point s=0, t=π2

Q: Let y = tan (3x + 3). Find the differential dy when x = 3 and dx = 0.4 Find the differential dy when…

A: Given is the function y=tan(3x+3) We need to find the differential dy when x=3 and dx=0.4. and…

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 partial derivative af for the function f(x,y) given below exp 2x. siny .(at the point (In2, 0

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Q: Let y = tan(5x + 6). Find the differential dy when x = 5 and dx = 0.2 Find the differential dy when…

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Q: Find at the point (1,0) for cos xy + ye* = 0. dx

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Q: B: Use the Chain Rule to find the derivative of f(x,y) = xy with respect to (t) along the path y =…

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Q: Use the appropriate form of the chain rule to find the derivatives. 5.x2 + 5y2 + z²; x psin ф сos 0,…

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Q: dt What is the linearization of h(x)= 6+ at x=1? cos (1 -1)

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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: Let y = tan(3x + 4). Find the differential dy when x = 4 and dx = 0.4 Find the differential dy when…

A: We know that, ddxtanx=sec2x We have,  y=tan3x+4 On calculating derivative with respect to x, we get…

Q: Let y=tan(3x+3). Find the differential dy when x=5 and dx=0.3  Find the differential dy when x=5 and…

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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: Differentiate implicitly to find dy/dx. cos(x) + tan(xy) + 4 = 3

A: Given: cosx+tanxy+4=3We need to find dydx.Recall the formulas: ddxcosx=-sinx…

Q: 5. Find dy/dx using implicit differentiation given x²y³ + cos y = 0.

A: Definition used -  Implicit differentiation -     It is a rule by which we can find the derivative…