Solve the second derivative forf (x,y,z) = sin* (x² +y²) a²f ax? x²+y² sin ت )م(. (x² +y²' sin sin 2(e cos² x² sin -2e A: (x² +y²' sin ** x² +y²' xsin sin x² +y² sin (x² +y² z cos(* +y?) (x² +y² cos2 2e +e 2(e (x² +y2 sin (x² +y² sin x² +y² sin cos² (x² +y²' +e z cos(+y²) (x² +y² x² sin -2e z sin x²+y² +e (x² +y² (x²+y² sin (x² +y² sin (x² +y² x²+y²) sin z cos( -2e D:2e 2(e E: none of above

Q: f(x, y) = ln (2x) In (3y) + x - y - xy - 3, then fyz (2,-) is equal to

A: Given :fx,y=ln2xln3y+x-y-xy-3

Q: 4. Find using derivative rules. dx sinx x8+x x2 tanx (a) y = (b) y= (c) y = cos³(3x² + 9) cos(5 x*)…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh x cosh(2x) = cosh2 x + sinh2 x

A:

Q: What is the maximum value of y = cos x. For - < x < < ?? 1 1/2 2.

A:

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A: derivative

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A:

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A:

Q: | 35. Prove the reduction formula for n > 2: cosh" x dx = cosh"- x sinh x + cosh" п-2 хdx п n-1 п п

A:

Q: Perform error analysis of approximation derived (a) 1 x² 1 - at xo = 0 X (b) sin (₁) ₁ X- at x = = 0…

A: Given that: a 1x2-1 at x0=0b sin xx-1 at x=0c exp x2-1 at x=1 and x=-1 The objective is to analyse…

Q: Differentiate : a. y= x^2 sinx +sin^2x + cos^2x + tan 2x/sin2x/cos2x b. y= In √x^3

A: a) y=x2sinx+sin2x+cos2x+tan2xsin2xcos2xb) y=lnx3

Q: 3G)Ú) Show that the reduction formula for atanx で-u sec"x dx = Sec" 「キu ) Hence use tthe formula to…

A:

Q: @Hiw/ prove that cosiz=coshz @ Cosh'z -sinh'z=1 @1-Tanhz Sechz D cos hiz-l = cschz COS 3 =- Sinh z…

A: (2) we have to prove that,                                                      cosiz=coshz we know…

Q: use the Mean value Theorem to establish Isine-siny </2-y) Ve,yER

A: We will prove the inequality as following.

Q: Find the derivative of O 2sec 2x 2tan 2x O-2 cot2x O 1/cos2x y=In sin 2x

A: I have stated the used formulas in the solution

Q: 2. Use the Intermediate Value Theorem to show that 2x-3 if – 3 0 has a zero on the interval (-2, ln…

A: Introduction: The intermediate value theorem is an advanced property of a continuous function.…

Q: ... at verifies the identity. OC. B. sin 9x cos 7x - cos 9x sin 7x = sin (9x – 7x) = sin 2x sin 9x…

A: Given query is to find the correct option to prove the identity.

Q: x2 f (x) = t² sin(2t) dt 1

A:

Q: 2- Find the third derivative for əx3 for f(x,y) = sin) )+2 sin) sin)+3cos°) 8y3sinz s()+2sin()…

A:

Q: The maximum value of y = cos x for - < x< is 1

A:

Q: 4. Find the first derivative of the given function using the Rules of Differentiation: sinx 2x-x-1…

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Q: The integration expression sin(3In(x) + 4)cos(3In(x)+ 4)dx must be transformed into using suitable…

A: topic- indefinite integration

Q: 3. Prove that cosh (2x) = cosh²x + sinh²x %3D

A:

Q: The integration expression sin(3In(x)+ 4)cos(3ln(x)+ 4)dx must be transformed into using suitable…

A:

Q: 5. Verify whether the function f(z) Cauchy-Riemann equations or not. sinh 4x cos 4y + i cosh 4x sin…

A:

Q: x'+y° Q4. If u = sin- sin-'( -), Show that x+y ди X- ди + y- = 2tanx (2 + ду

A: If u=sin-1x3+y3x+y, then show that x∂u∂x+y∂u∂y=2tanx.

Q: Let f : R→ R be a differentiable function. Then for all x € R, the derivative of f ( sin (4x)) with…

A:

Q: 3. Prove that coshx – coshy = 2sinh () sinh ().

A: As per honor code we are entitled to solve only 1 question at a time so I am providing you the same.…

Q: The integration expression sin(3In(x) + 4)cos(3ln(x) + 4)dx must be transformed into using suitable…

A:

Q: What is the derivative of f(x) =2cos (x)? %3D 2 cos (2x) O -2 cos (2x) O 2 sin (2x) -2 sin (2x)

A: f(x) =2cos2xdifferentiating w.r.t xd(f(x))dx=ddx(2cos2x)

Q: 5. Let F(x) : = a sin(3.x) + bx cos(3x). Find constants a, b such that F'(x) = 2x sin(3x) and verify…

A: The detailed solution is given below Thank you

Q: a 5. Using integration by parts twice, prove that the L (sin ax) %3D s2+ a=

A:

Q: 1) sinh-1x = In(x + Vx² + 1) %3D 2) cosh-1 x = In(x+ Vx² – 1) %3D 3) tanh-1x In ) X = 1-x

A:

Q: Use the Second Derivative Test to find all relative extrema. (a) h (x) = x - 2 cos x, [0, 4π]

A:

Q: (a) Evaluate the indefinite integral (anti-derivative) x°(1+ 2*)® dx by using the substitution u =…

A:

Q: Find the derivative of cos(In(x)) ((x)soɔ)u| cos(In(x)) – In(cos(x)) sin(In(x)) cos²(In(x)) A cos…

A: The objective of the question is find the derivative of the given function.

Q: Express limn→∞∑i=1nsinxiΔxlimn→∞∑i=1nsin⁡xiΔx as a definite integral on the interval [0,π][0,π].

A:

Q: у %3DIn(In sec x)

A:

Q: (2x) Sinx 2. Prove that (1) Jy₂ (x)=√√(x) =_ (11) J-y₂(x) = √(3/1²) Cosx

A:

Q: Find dy/dx using appropriate derivative rules. 1. y = 8x^5/2 - 7x-9 + square root of 5 2. ) y =…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: The derivative of sec² 2x (cos² r - sin² x) with respect to a is O2 sec 2x tan 2x O4 sec² 2x cot 2x…

A: Find the derivative

Q: Differentiate the function. f(x) = sin(x) In(3x) sin (x) f '(x) + cos (x) In (3x)

A:

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A:

Q: 1: Find the derivatives of: 1+ tanh x a) y = In ソ= %3D 1- tanh x b) 2 y= cosh? 1-x? 1-x

A:

Q: Find the derivative of f(x) = ecos² (3x+1) Of(z) 6 sin(3r+1) cos(3x + 1)ecos² (3+1) O (E) None of…

A:

Q: Prove cosh 2 x - sinh 2  x =1

A: To prove  cosh2x-sinh2x=1

Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

Q: Use integration by parts to verify the reduction formula.

A: We have to verify the reduction formula using integration by parts, ∫cosn x dx=cosn-1 x sin…

Q: (b) Verify that f(x) = 2 cos(x) sin(x). f(x) = sin(7x) + sin(8x) 7x + 7x = 2 sin 2 = 2 sin |co(-)

A: Let the function is  f(x)=sin(7x)+sin(8x)   Formula used: Sin(a)+sin(b)=2sina+b2cosa-b2

Q: limit x approaches zero, sin^2x/x

A: Given,

Q: 1. Find the numerical Integration of cos(x) + sin(x) where n = 4 using trapezoidal rule.

A: