D. If z = In(x – y) + tan(x + y), show that Z = Z y XX

Q: Show that d (x + 1)? 1 (을 tan 'x + t In dx (1 + x)(1 + x²) x? + 1

A: The given function is

Q: Let V = eP cos(qr), with p = x In(xyz), q = z cos(Ty) and r = 2 tan-(y). By using the chain rule,…

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Q: 7. Determine f (x) so that cos(In'x) f(x) dx = sin(In'x) + C %3D (a) 2 In x 2 In x (b) (d)

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Q: Let ro)-플-x a-글 FW) = b = 0, and n=3. Then: cos (f(x))dx =

A: We can find the integration as below

Q: If z = In(x – y) + tan(x + y), show that Z = Z, XX

A: We have to show that given expression.

Q: Find y if: (a) y = (In x)cOs z (b) y = In(x² + y²> %3D

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Q: Suppose z is a function of x and y. Solve for ∂z/∂y if tan √(y^2 + x^2 + z) = z^(x)e^(6y).

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Q: Use the substitution t = tan(x/2) to find the integral: 2 1+2 sin a dr Cos I

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Q: dx Evaluate: J sin x A. 3tan'x ++C C. tan'x +C tanx tan x + C tan 2x D. в. 3tan'x tanx 2tan2x

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Q: 2. (a) Let f(x, y) = x² sin(x + y), find 잃 and 잃.

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Q: Which is the du in y= sin (x2-2x + 1)? x2-2x + 1

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Q: 1. If y= tan x, prove that y"= 2(y² +1)(3y² +1).

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Q: Let y = (sin z+ cos r)e", x E [0, 27]. %3D

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Q: If f(x) = 5 sin x + 12 cos z, then %3D f'(x) = f'(2) =

A: The question has been solved in detail in the next step.

Q: Let h(z) tan(5x + 5). Then h' (2) is and h'' (2) is

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Q: Evaluate: Sv*+sin/x dx. A x+2cos/x+ C 2x+ cosx B + C 2

A: We have to solve the integral

Q: 1. If y= tan x, prove that y``= 2(y² +1)(3y² +1).

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Q: 3. Let G = {z = x+iy : x < 0 or y # e" sin x}. Show that G is simply connected.

A: Given: G=z=x+iy; x&lt;0 or y is not equal to ex sin x

Q: If u = x² tan equal to (a) (c) x - y x + y - 2 + V² 2 X X -, y x + y x - y x² + y² 2 X - y - y² tan…

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Q: 3. Let V = e" cos(qr), with p = x In(xyz), q = z cos(ry) and r = 2 tan-(y). By using the chain rule,…

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Q: 2.xy x² – y? Show that - = 0 if z= Tan

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Q: bx + c Given tan 3 - In(x2 - 8x + 25) + 1 -dx %3D x2 - 8x + 25

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Q: D[Expf-3x] Cos(nt], {x,2},t]

A: Correct option is D

Q: Let z = e* + In( y), x = sin (uv), y° = cos (uv). 2 Determine at u = 1, v= 3

A: Topic- partial derivatives

Q: The substitution u = tan |converts the integral 2 π/3 1 dx to: n/2 2 +sin x - coS X

A: Given,∫π22π312+sinx-cosx

Q: Find * if y = y(x) on D is the domain of y(x). (II) (B + 2)y(«+1)cos[(a + 2)x] = x(«+1) + sin [(ß +…

A: Take the derivative of each term and than simplify.

Q: Find F'(x), f"(x) and f'"(x) for f(x)=x$+cos(9x).

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Q: The f xcos x² 1-sin x2 dx is

A: Given :

Q: 220. Suppose f(x, y) = x + y, u = ex sin y, x = 1², and y = лt, where x = r cos and y = r sin 0.…

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Q: Evaluate si (z* - tan(z) cos(z) ) dx 2-1

A: To find the integral: ∫11x2-tanxcosxx3-1dx

Q: Let f(x) = w when 0 < x < a and 0 otherw 00 w sin ak cos()dk =

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Q: Let z be defined implicitly as a function of r and y by the equation dz 4+ In (xy?) – cos (xy – z) =…

A: We know that (u·v)' = u·v' + v·u' ddxtanh-1x = 11-x2 ddxfu(x) = dfdu·dudx      (chain rule)   Given…

Q: Let z be defined implicitly as a function of x and y by the equation dz 4+ In (xy²) – cos (xy – z) =…

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Q: If f(x) = 6 sin z + 6 cos z, then f'(x) = %3D f'(5) =|

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Q: Given f(x,y) = eX cos y, Evaluate fy(2,0) O cos 2 O sin 2

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Q: Let f(x) = e cosx, sx %3D 2. Express your answers in exact form. ElN

A: Inflection point occurs when the second derivative of the function equals to zero.

Q: dz Let z=sinh -(y-2x), where x = we and y=In then is given by du

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Q: 22: Find dyldx for the following functions * (40 marks) · y = In (3 – 4 cos x) + (4x – 5)5 2. y = x²…

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Q: If z=x+iy=r(cos(0) + isin(e))then

A: The given equation is z=x+iy=rcosθ+isinθ.

Q: - Find + Uy, Given that u(X,y) tan(x+11XY+y")

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Q: If y= tan x, prove that y 2(y² +1)(3y² +1).

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Show that w°sin(xw) пе dw= 2 cosx if x > 0. w* + 4

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Q: 1. If y= tan x, prove that y= 2(y´ +1)(3y² +1).

A: Use the following differentiations as, ddx(tanx)=sec2(x)ddx(sec(x))=sec(x)tanx Now, differentiating…

Q: If w = Vr + y² + zª where r= sin(0), y = cos(@) and z = Use the Chain Rule to find tan(@). dw when…

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Q: Let z=In(x²+y²) where x=ue"sin t and y = ue"cos t. If u=- 2 and 1=0 then is equal to %3D ....

A: Multivariable function: When a function f has more than one independent variable and only one…

Q: 1 Use the substitutions given to find fI+x dx; u = 1 + x + sin x dx; u = sin x cos x a

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Q: . If f(x, y)=x² cos y-y° sin x- xe" – ye* +2x²y² , show that ôxôy a²ƒ_ ô²ƒ дудх

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