Compute sryds the line intogal where C: r(t) = (sin(xt), cos(at)) I≤ t ≤T 2

Q: 14. ry = coS

A: Given:      xy=cos-1xy+1        y=cos-1xy+1x differentiating on both sides     dydx=ddxcos-1xy+1x…

Q: The y - cos X 3 2 =2y %3D

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Q: What is the derivative of y = 3x²tan-1(x)?

A: ddxxn=n xn-1ddxtan-1x=11+x2 One have to use product rule here, which is ddx(uv)=vddxu+uddxv

Q: The maximum directional derivative of f(z,y,2) sin(zy)-ya +10 at (-1, 2, 0) is Question 5

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Q: 5. gl1) = Cot3x ら。 -- HQ) = I+ Sin x 1- Sin X

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Q: Express the following function in the form f(z)=u(x,y)+iv(x,y) 1. cos(z^2)

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Q: QIFind the derivative of the function f(z, k) = z* – 16k + tanh(z) – 4 csc(k) in terms of z and k ?

A: Dear student  Here is the solution of your query

Q: Define a function f : R² → R² by f 2.у 1. Show that f is differentiable on A = E R² |x > 0, y > 0}…

A: To show that the function f defined as below is differentiable on A and compute its derivative

Q: dy Find for the given implicit functions: dx а) у? - ху%3D2 b) 2.x sin (xy)– x = 0 c) (xe')" + y = 3

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Q: 5. Find the following derivatives: a) y = x?e-2/x b) y = t tan -t- t -Int

A: Given:  5)a) y=x2e-2xb) y=ttan-1t-12lnt To find: Derivatives of the given functon.

Q: Find the derivative of y. 30) y = In (sinh 5x) D . sinh 5x A) coth 5x B) 5 csch 5x C) 5 coth 5x

A: We can answer the question as below.

Q: B) Find- for following functions: дz მა 1) z = exy tan y, x = s + 2t, y = s/t. 2) z = x² + xy + y²,…

A: The objective of the question is evaluate the partial derivative of the given functions.

Q: (3/5) What is the directional derivative Duf at the point (3, 1)? Let f (x, y) = x² - y and u =

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Q: alu,v at dx,yl Q2// B :- If u+v=e"cos y and u- v=e" sin y find the Jacobain of the function (х,у)…

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Q: Apply Euler method and Richard son extrapolation anthe problem ity: y' = 1+t year=o. and approximate…

A: Definition anf formula;

Q: Find extrenhum of one of the following function 1. 2(a, y) = sin2(x- 0.5) + artg (y- 0.5) rE (-1,1],…

A: Let us find the Extremum of the given function in the next steps.

Q: Let z = In(x² + y²) be a differentiable function of x and y, where x = sin t, y = cos t. dz when t =…

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Q: 12. Find frxyz for f (x, y, z) = sin (3x + yz)

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Q: Calculate dwldu and using the following functions: = f(x, y, z) = 3x2 – 2xy + 4z2 x(u, v) = e" sin v…

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Q: 5 dy of: y = |x sin 2 + tan (x") dx 4

A: Given function is y=xsin2x+tan4x75 We have to find dydx. Here, we have to use some rule of…

Q: 8. What is the derivative of y= Vu in terms of x? dy a) 2/y dulas b) 2vu d) 2/u

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Q: 1/2 105. Show that f (sin 0) de = f (u)- 1-и2 du.

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Q: For the function shown bellow; Find the second order derivatives : af/ay (a^2 f)/(ay^2) f (x, y) =…

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

Q: Differentiate the following function.   r(t)=(t e^-t,5tln t,t sin t)

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Q: Vリ What is F'(;) 4 ? 16 π 4 π ミ|N

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