If h(z) = sin (z) + sin(z°), find h'(z). a. 6s in (z)cos(z) +6z°cos(z°) Ob.6cos (z)sin(z) + 6z°sin(z°) Oc 6sin (z)cos(z) – 6z°cos(z°) O d.6sin (z)cos(z) – 6z°cos(z°)

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Q: 1. Given that x = 3 cos nt, y = 3 sin at and z = 4nt with 0<t<1. Evaluate (x + z) ds.

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Q: S sin(ln x)dx A 1 x sin(lnx) – cos(Inx) + C x sin(lnx) – cos(lnx) + C| B D x sin(Inx) + cos(Inx) + C…

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Q: 14. Find the antiderivative of 5sinx In 5 cosx. a. 5cosx +3 c. 5sin x In b. 5sinx-2 d. 5 sin x + 7…

A: Anti derivative of the function

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Q: (d) Re(cosh z) = cosh x cos y, Im(cosh z) = sinh a sin y. (e) | sin z|? = sin² x + sinh? y, (f) |…

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Q: O(y-+ rycota)dr + zdy O (coszcosy– cotz)dr sinrsinydy 0 O ydr + (3z -g')dy = 0

A: A differential equation is called linear if 1) every dependent variable and derivative involved…

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Q: if y= tan (cos(u)), u = cos )and t In(x2) dy then when x Ve is -8 5Ve 8 5Ve 4 5Ve -4 5/e

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Q: Solve the D. E. to the I. V. P. sinx(e + 1)x'- cosx 1, y() = 0 O (1 + e') (1 + cos x) = 2 O (1 + e)…

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Q: Solve the D. E. to the I. V. P. sinx(e + 1)x' – cosx = 1, y(0) = 0 COSX O In (1 + cos x) = 1 + e (1…

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Q: ди k > 0 at Ans. u = e'(A,eka! cosh ax + Bjekai sinh œx) u = e¯'(A2e' u = e"(Azx + B3) k ¯kai 'cos…

A: The given problem is to find the solution for the given partial differential equation in different…

Q: B. and , if z = (x² + y²)³/2, and r = e-" sin v, y = e¬u cos v. В. %3D

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Q: Let y(x) be the solution for the DE. y +y tan(x) + sin(x) = 0 If y(0) = In 2, then at x = %3D - 4…

A: We have to solve given problem:

Q: /hich of the following does not require the use of the dy nain rule to find ? dx A y = cos1 (10x –…

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

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

Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: 13. For J* sin x dx, what is u? sin x dx 2x dx -x cos x+ 2x sin x+2 cos x +C Oc. OD.

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Q: 6. If w=xy + yz + zx. x =r cos0, y = r sin0, z= r0, Find dw/dr, dw/dO, when r = 2,0 =x / 2.

A: Answer

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: 2. The antiderivative of cos Π.Χ. A. -cos 2 B. KIN COS C. sin D. sin π.χ. is

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Q: The "equation cos x "y sin x is A Iny In (cos x) + k B Iny = In (sin x) + * c. Iny=-In(sin x) + k…

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Q: Given z(x, y) =In(2xy) where x(u,v)= e" cos(4v) and y(u,v)=e" sin(4v). Find ди 1 cos (4r)+-sin(4v)…

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Q: Find if z = sin(uv)cos(uv), where u = e' and y = e2t. dt %D Lütfen birini seçin: O A. 3e(sin2(e3t) -…

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Q: The acceleration ā of a particle at any time t is given by à = e-2 î + 3t ĵ+cos t k , then the…

A: The acceleration of a particle is given by a→=e-2t i^ + 3t j^ +cost k^  v(t) = ∫a(t) dt = ∫(e-2t i^…

Q: 1 The value of S dx at x=0 is sinx+cosx C V7 (Inv2+1) +c Cn|vZ+ 1] +c ㅇ글미VZ+ 1| + c c -공in(V2+ 1) +…

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Q: Let y(x) be the solution for the DE. y+y tan(x) + sin(x) = 0 If y(0) = In 2, then at x = %3D %3D the…

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Q: əz Əz Əx Əy Q5-A) If z =(x +by)² +e+by+sin( ax +by) show that b =a

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Q: What is the general solution of sin z sin ydr + cos zcosydy =0 tan z = C sin y + cos r + C sin z = C…

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Q: Given: x = 0– sin 0; y = 1– cos 0 d'y Find: dz2 d'y dr? (1-cos 0) CO d²y dr (1-cos e) (1- -cos 0)…

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Q: 2. Find the length of the asteroid x = cos't and y=sin't , 0<t<2n. x = cos' t y = sin³ t

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Q: If z = x2 + y?, x = e' cos(s) and y = e' sin(s), then %3D dz at (t, s) = (1,0) is as %3D

A: Given that z=x2+y2, x=etcoss and y=etsins First we have to find ∂z∂s.

Q: If f(z, y) = e sin 8y, then fzy is given by: O 16 e sin 8y 16 e sin 8y O 16 e cos 8y 27 16 e cos 8y

A: We can solve it by taking partial derivative of both side two times as below

Q: The function z = cos 0, y = sin³ 0 where 0 < 0 < 27. Use the x2 Vy is defined on the astroid x = dz…

A: The chain rule is stated as follows:

Q: If z = x2 – y2 and x t cos 2r and y = r sin t, then %3D a2z is ar2 (A) 2 cos (2r) + 2r? cos?(t) –…

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Q: 1) Given x = Vu2 + E2 sin 0 cos 2 y = yu? + E² sin 0 sin 1 z = u cos 0 ds? = dx2 + dy2 + dz2 %3D…

A: Hi! As per norms, we will be answering only the first question. If you need an answer to others then…

Q: Solve the D. E. to the I. V. P. sinx(e¬ + 1)x' – cosx = 1, y(곡) = 0 - O (1 + e') (1 + cos x) = -1 O…

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Q: If z=1+y , I= e' cos(s) and y=e' sin(s), then at (t, s) = (1,0) is as O-2e O 2e O 2e

A: if z=x2+y2 where x=et coss , y=et sins then find ∂z∂s at t,s=1,0

Q: (b) If u = x² cos y+ye", where x = s+2t and y = st, prove that ди ди 2 = (s – 2t) (x siny– xye –…

A: u=x2cosy+yexyx=s+2ty=st

Q: Following S sin(A) cos(B) dx = ; f sin(A + B) + sin(A – B), | what is the integral of f sin 5x cos…

A: We have to solve the following

Q: Solve the D. E. to the I. V. P. sinx(e + 1)x – cosx = 1, y(0) = 0 COSX In (1 + cos x) = 1 + e² O (1…

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Q: Find ∂w∂s and ∂w∂t when s = 1 and t = 2π for w = xy + yz + xz                    where x = s cos…

A: Given: w=xy+yz+xz where x=scos(t), y=ssin(t), z=t at s=1 and t=2π

Q: When J x°cos (x-)dx is evaluated using IBP, the value of J v du is? A - cos (x2) B none of the…

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Q: The function z =x^2√y is defined on the astroid x = cos^3θ, y = sin3θ where 0 ≤ θ < 2π. Use the…

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Q: If z = x2 – y2 and x = t cos 2r and y = r sin t , then a²z is (A) 2 cos?(2r) + 2r² cos²(t) – 2ry sin…

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Q: fip Ify r' sin I, dx a)3x²+ cos x 3. O b) 3x sin x + x° cOS I O cos x 3x sin x + x³ COS 2 Od 13…

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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: 2 tan-1(y). x In(xyz), q ƏV when x = y = % = 1. ду Let V = eP cos(qr), with p = z cos(TY) and r = By…

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Q: 7. Determine the following general antiderivatives. | cos*(x) b. sin(x) xp- 10 10 | sin(x)cos(x)] d.…

A: Please see the below picture for detailed solution.