If z = In(x – y) + tan(x + y), show that Z = Z, 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: Find y if: (a) y = (In x)cOs z (b) y = In(x² + y²> %3D

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Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: 2. If f(x, y)=x² cos y-y' sin x-xe'-ye* +2x*y', show that ôxôy ôyôx

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Q: Find the Wronskian for the set of functions.{1, sin 2x, cos 2x}

A: Here the given function  {1, sin 2x, cos 2x}

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: If g(x) = f'(x) and if g(x) = (cos x – x sin x)e*cosx, then S g(x) tan(f(x))dx is x cos x

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

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

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Q: 2. If f"(x) = 4 sin x +16 cos x, f(0) = 6, f'(0) = 1, find f(x) and f ().

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Q: Prove that sin x can be approximated by x − (x^3/6) within 0.01 on the interval [-1,1].

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

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Q: If F(x,y,z)=sin(x³y²)+cos (Vxy2)+x®y²z, then fyz(1,-2,1)=

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Q: y = x cos(In x)+x² In x²

A: d dx(cosx) = -sinxddx(lnx) = 1xddxx2 = 2x   Product rule u.v = u'.v + v'.u

Q: dz and du dz Find when u = In 2, v = 1, if z = 10 tan'x, and x= e" + In v. -

A: Here we the chain rule to get the answer .

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sin-1 (xyz)

A: Given that f(x,y,z)=sin-1(xyz)

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

A: Correct option is D

Q: 1+ In x Find f(x) so that when u f(x) the integral tan( fx) dx can be rewritten as cot u du. A) x-…

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Q: Suppose that w = a7 · exp(2y) · cos(4z) with z- in (+ 5), x = sin (t+ y = In (t +2), z = t.

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Q: Define h(x) = x³ sin(1/x) for x + 0 and h(0) = 0. By using the product and chain rule we know that…

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Q: Given that: z = y sin(2x) + (1+x²)e* + cos x tan¬1(y* + 1) In(y6 + 137)

A: z=ysin2x+1+x2ex+cosxtan-1y4+1lny6+137 Differentiating wrt x, we have…

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

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Q: The f xcos x² 1-sin x2 dx is

A: Given :

Q: If g(x) = f'(x) and if g(x) = (cos x – x sin x)e* cos x, then S g(x) tan(f (x))dx is

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

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

Q: Suppose that w = x² + y? + z², x = cos 0, y = sin 0, z = tan 6. Use the chain rule to find dw when 0…

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

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Q: 7. Determine f (x) so that | cos(In°x) f (x) dx = sin(In²x) + C 2 In x In x (а) 2 In x (c) - (d)?

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Q: If f(x) = 3 cos(3 In(x)), find f'(x).

A: Consider the function  f(x)=3cos3ln(x)

Q: Let f(x, y) = 2e sin(4) of д х of dy Check Answer

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Q: Find ſ z2 sin z dz

A: We can find the integral in the following steps

Q: Evaluate (cos x)(n sin x)dx. А In V sin x + C В sin x (1 – In sin x) + C C sin x (1 + In sin x) + C…

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Q: (a) If u(x, y) = cos-1*" + y* ) x² + y? = COS then prove that ди du + y = -2cotu

A: Given: ux,y=cos-1x4+y4x2+y2

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

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Q: If f(x,y,z)=In(x²y+sin?(x+y))+111x112y2z113, then at (1,1,1) is equal to əx²əyəz

A: We have to find derivative

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: Q6:-Prove that: y" = 1 y =csc(tan"" ) if

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Q: Express T(x)sin x-root(3)cos x into the form of T(x)=Asin(x+theta) , where A>0

A: Sin(A+B)=sinAcosB + cosAsinB

Q: Use the Intermediate Value Theorem to show that sin x x2 – x has a solution on the interval (1, 2).

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Q: Find all values of in the interval 0, 2 such that sin x = sin 2x

A: To find all values in the interval for the function

Q: Prove that d/dx [cos x] = −sin x.

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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: csch(3 tan x) + sin² x cos² x dx

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Q: Given that: z = y sin(2x) + (1+x²)e* + cosx tan¬(y* + 1) In(y® + 137)

A: ∂z/∂x  is the partial differentiation of function z with respect to x, keeping other variables…

Q: Let = (sin x cos y, cos I sin y, In z).- Compute div i %3D

A: Given,          v→ =  sinxcosy , cosxsiny , lnz