2. f(x,y) = 1- x² – y², find fx and fy ди 3. u = 2x(sinx?y), find ди and ax ду 4. f(x, y, z) = x cos z + x²y³e², find fx, fy and fz " and ди du 5. u = , find x+y ду ax

Q: In Exercises 61-68, compute the derivative indicated.

A: We have solved first three parts for you, if you want solution of other questions, repost them.…

Q: f z = e^(-t)(\sin x+\cos y), show that (∂^(2)z)/(∂x^(2))+(∂^(2)z)/(∂y^(2))=(∂z)

A: Given  z = e-t ( sinx + cosy)∂z∂x = e-t cosx,   ∂z∂y = e-t ( -siny ),  ∂z∂t =- e-t (sinx + cos y )

Q: Compute div F, where F(x, y, z) = (x² + 3y, y? – 4z, sin r cos y – 22). A. (4 – sin r sin y, – cos r…

A: Given : F(x, y, z)=(x²  + 3y ,  y² -4z ,  sin(x )cos(y) - z2 )  Now we find div F = ?

Q: Given that z and w are independent variable and dependent variablerespectively, obtain dz/dw a.…

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: 2- find if z = x + 2メッ ze %3D U COSU = u sinv

A:

Q: Evaluate F. dr where F(x, Y, z) = (1.25yz cos(xyz), 1.25xz cos(xyz), 1.25xy cos(xyz)) 1 1 and C is…

A:

Q: The equations re + uz – cos(v) – 2 = 0 and u cos(y) + 9x?v – 3yz² – 1= 0 can be solved for (u,v) as…

A:

Q: If z = x2 + y² and x t cos 2r and y = r sint, then %3D a2z is at2 (A) 2 cos²(2r) + 2r? cos?(t) – 2ry…

A: Given  z=x2+y2      and x= t cos 2r ,y= r sin t First substitute x,y values in z  Then derivative…

Q: 2. Let f(r, y,z) = In(r² + 2) + ye* – cos(2yz). Find faya- COS

A: see below the answer as per bartleby guideline we have to solve the first question onl

Q: Suppose f(x, y) : where x = r cos 0 and y = r sin 0. 4 af af and ar Find when r 1, 0 -

A:

Q: Find the orthogonal trajectory of y = C[cos(5x – 1)]. O y? = In [sin(5x – 1)]² + C O In[- cos(5x –…

A: The given equation is, y = C[cos(5x-1)]-1

Q: Find y' (or ) if In(21y) sin z = zy4 + 8z5 y5-yln(21y) cos z+40z4y sin z+4zy4 y5-yln(21y) cos…

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

A:

Q: dy Find as a function of x when y = sin°(x) %3D O 1) 5cos (x) 2) 5sin (x)cos(x) 3) 5sin (x) 4) 5cos…

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Q: Show that - if W= cos (メ+y)+ Sin(メ-y) Wメメ Wyy ニ

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Q: A force of F(x)=x2−cos(3x)+2, x is in meters, acts on an object. What is the work required to move…

A:

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: 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: Inz Vz Inz-z dz 2. Je cos 3r dz 13. S- ze-lal dz 74: cscz cot z dz dr dz dr 3/2 dz 26. J. v9-2 6.…

A:

Q: 3z2 If f(z) = | cos(t) dt, then f'() = %3D %3D Select one: a. 6z cos(9r) b. 6z cos(a?) c. 3z cos(r?)…

A: Leibniz rule of differentiation: ddx∫uxvx ft dt=fvt.dvdx-fut.dudx

Q: az Find when u = 0 and v dv 117 if z(x, y) = sin x + cos y, x = u •v, and y =u + v.

A:

Q: find fsub(x), fsub(y), and fsub(z): f(x,y,z)=e^yz+sinx)

A: Given,          fx,y,z=eyz+sinx

Q: Find y' where y = 8 cos-1 (sin (19 z)) – cot-1 (14 z) Answer: 14 y' = -152 1+196 z2 -152 cos(19 z) +…

A: This question belongs to derivative of inverse trigonometric function.

Q: Ex: If w cos(uv), u = = xyz, y = π 4(x²+y²)' aw find at point (1, 1, 1). əx

A:

Q: azu azu (a) Verify that u satisfies ax2 = = 0 , if u = e* sin y. ay?

A: NOTE:Kindly repost the other question as a separate question.

Q: Suppose f(x, y) = x2 + y? where x = r cos 0 and y = r sin 0. af and Or 1, 0 = 6 Find -when r

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Q: 3. Given that z= (u, v), where u 2r cos y and vz sin y. Find and Hence, show that Dy

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Q: cotu. vX + vy + y %3D If u = show that x ax ay = CoS coS х - у

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Q: bot A de groutne conitant. est Cheafuntis uh that f cark3 and f'4)=-s. g(xl=In (f(x)) + A conx)

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Q: If, for V = V (t), tsin(V) = cos(V)+ In(t), then: a) V'(t) = 1 – tsin(V) t(t cos(V) + sin(V)) b)…

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Q: Determine the concavity of y = 3 + sin x on [0, 2π]

A: The function y=3+sinx on the interval 0,2π. We have to determine the concavity of this function.

Q: Use Cramer's rule to solve for x' and y' in terms of x and y. x = x' cos 0 – y' sin 0 y = x' sin 0 +…

A: Solution is given as below:

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: (a) Prove that dv 1 2 u? + v2 arctan u- + C. 2 u 2, /2/2 ru (b) Prove that I dv du 2 - u? + v2 18 by…

A:

Q: L'équation 5xyz = 2x2 + y² +2z² + 6 définit implicitement z comme fonction de x et de y au voisinage…

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Q: 2. If o = x²yz³ and F(x,y,z) = 3yzi + x²j + (x cos y)k, find: a) grad o %3| b) div F c) curl F

A: Given:  φ=x2yz3F→x, y, z=3yzi→+x2j→+x cos yk→ To Find:  a grad φb div F→c curl F→

Q: Q1: show that1) d/dz [cosz] = -sin z, %3D 2) 1+tan2 z = sec2 z

A: solution

Q: -1 If cos x+cos y+cos z= T, prove that x +y +z +2xyz = 1

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Q: If z = exy where x = In(u + v) and y = sin(u-v), find az and az du

A: We use the partial derivatives and chain rule of differentiation to answer the given question.

Q: 10. If e is the acute angle between the surfaces xyz = 3x + and 3x - y + 2z = 1 at the point (1 -2…

A: We have to solve given problem:

Q: For u = ex cos y,(a) verify that ∂2u/∂x∂y = ∂2u/∂y∂x;(b) verify that ∂2u/∂x2 + ∂2u/∂y2 = 0.

A: The given  function is, u=excosy (a) To verify ∂2u∂x∂y=∂2u∂y∂x Solution: We have u=excosy…

Q: find the local extrema with (binding) g = 0.

A: To determine the extrema of the function f(x, y, z) subjected to the constraints g(x,y,z)=0 Write…

Q: 26. /(х, у) — х 27. f(х, у) — sin y 28. /(х, у) — х1 + 9у2

A: fx,y=x fx,y=siny fx,y=x2+9y2

Q: aw 4 - find zu me aw i f w : tan () and X = U COSU y = u sinv .

A:

Q: fe and dr af Consider f(x, Y, z) = x² + y²z² and r = rsin 0, y = r cos 0, z = Or³. Find

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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: