dy Find as for y = x - x sinx O 1) - 1 - 3x² cosx - x³ dy sinx dy O 2) = 1 - 3x² sinx - x³ cosx ° cosx O 3) = 1 - 3x² cosx - x³ cosx dy COSX O 4) dy dx = 1 - 3x2 sinx - x sinx

Q: find dy/dx.1. y = -10x + 3 cos x            2. y = 3/x + 5 sin x3. y = x2 cos x…

A: Given the functions :- 1.  y = -10x + 3 cos x Differentiating with respect to x dydx =…

Q: (2y cosx + sin“ x)dx = sin x dy ,when x =",y = 1 5y= 1 %3D X 2

A: 2ycosx+sin4xdx=sinxdy,   x=π2,   y=1:A first order linear ODE has the form of y'x+pxy=qxLet y be the…

Q: Find if x2y - sinx - cos y dy dx O dy da 2xy x² COS sin y 10.

A: Given: x2y-sinx-cosy=10. Now,                x2y-sinx-cosy=10Differentiating both sides wrt…

Q: af dy %3D Y Given f(x, y) = 17x² sin y then 17x2 cos y O -34x cos Y O -17x² cos Y 34x cos Y II

A: The function is given by fx,y = 17x2siny To evaluate : The expression of ∂f∂y

Q: * Find dy/dx for the function y=2 sin(3x) cos2x 4 sin (3x) sin (2x) - 3 cos (2x) sin (2x) O 6 cos…

A: We know that derivatives  general power rule is - d(xn)/dx = nxn-1. And d(sinx)/dx = cosx ;…

Q: What is the dy/dx of y = 3sin²x cos x ? O 3 sin x(sin²x - 2cos²x) O-3 sin x(sin²x - 2cos²x) O 3 sin…

A: Given: y=3sin2⁡xcos⁡x To find: dydx We know that ddxcosx = -sinx ; ddxsinx = cosx

Q: dy Find ax for y = cosx(1 + cscx) dy O 1) = -sinx cscx cotx %3D O 2) 2) dx = -sinx(1+cscx)-cosx cScx…

A: Given, y=cosx1+cscx We have to find dydx

Q: cos² (6y) + sin²(6y) = y + 12.

A:

Q: Find the solution. (y - x- xy cotx) dx + x dy = 0 A) xy sinx = c + sinx - xcosx B) xy cosy = c+ sinx…

A:

Q: If f = 5x2y2 - XY2 then find af at (3,1) %3D dx

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Q: Find Fxx and Fxyz of: XX хуz y2+Cos (xz) f (x, y, z) : 2 Siny

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Q: 4. (2y cos x + sintx) dx sinx dy 5. y' = 1 + 3ytanx %3D

A:

Q: Find Duf at P: f(x,y) = sin(8x – 5y); P (5,8); fi-) U =

A: we can solve this as follows:

Q: 7 show that: sech x dx = Sin (tankx). √1-u² multiply note: * & Sim'u = dx * you Cam سال dx sechx by…

A: Differentiate rhs

Q: Find fy ) for (x,y) Cos (x) sincy) exy

A: Given query is to find the partial derivative of the expression with respect to y.

Q: Find dy/dx 1. sin^−1(xy) = cos^−1(x − y) 2. sec^−1(2y cos x) = x^y

A:

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

A:

Q: cosxdx 17. - secx+ tan x [2sin(3x)cos(5x)dx 18. [(sin y +2cos y)'dy 19. 20. ſcot'(2x)dx 21. (sin“…

A: solution is given below

Q: tep 5 of 5 Substitute appropriately tan(xy) = x2 sec?(x²y) dy + 2xy sec2(x²y) and dx -(7x + 8y)3 =…

A:

Q: (1-1/2 x^2)cos x 3. y = 2cosxsin2x-sinxcos2x 4. y= x^3 - x^2cosx + 2xsinx + 2

A: Differentiation: 1.y=sinx2+cosxdydx=(2+cos x).cosx-sinx(-sinx)(2+cos…

Q: Ssin x x cos x dx = %3D Select one: а. -cos 2x +C 4 b. -cos x + C 4 c. -sin 2x + C 4 d. -sin x + C 4

A: We need to evaluate the following integral ∫sinxcosxdx

Q: - (2y cosx + sin* x)dx : sin x dy, when x =y= 1 %3D

A:

Q: cosxdx 17. secx+ tan x 18. [2sin(3x)cos(5x)dx 19. [(sin y + 2 cos y)'dy 20. ſcot'(2x)dx 21. [sin“…

A:

Q: y = cos“ x, Find dy/dx O dy = - sin(x*) O dy = 4 cos3 x sin x dx O dy = - 4 cos x sin x dx O dy = -…

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Q: dy Find ax for y = sinx tanx %3D dy 1) dx = coSx sinx - sinx târdx sinx tanx O2) dy dx = CoSx tanx -…

A: I have stated the used formulas in the solution.

Q: Let 6 sin x + 7 cos y = 7. dy (6cos(x)csc(y))/7 dx dy = dx2

A: Simply take the derivative of the whole expression with respect to x than simplify.

Q: Let 6 sin x +7 cos y = 7. dy (6cos(x)csc(y))/7 %D dx dy dx2

A:

Q: (2y cosx + sin* x)dx sin x dy, when x = y = =,y= 1

A: Given - 2ycosx + sin3xdx = sinx dy , when x = π2, y = 1 To find - Solve the following differential…

Q: Find where y(x) is defined by d²y dr? (a) 3x2 – e2, (b) sin 3x + cos r, (c) 1+x – x2 + In r. - -

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Q: 1. y = (3x² + 3x - 1)4 2. y = (5-2x)-2 3. y = cos3 (πx)

A: Disclaimer: Since you have posted a question with multiple questions, we will solve the first three…

Q: Suppose x and y are variable (y is a function of x) that satisfy the equation Sin(x +y) =xy, What is…

A: We have to find derivative

Q: Find the solution. (y - x+ xy cotx) dx + x dy = 0 xy cosy = c+ sinx - x secx B) x siny = cx+ sinx -…

A: The given differential equation is y-x+xy cot xdx +xdy=0. The integrating factor of the linear…

Q: Let f(x, y) = 3e" sin(5y) af af dy

A:

Q: The integrating factor of the linear first order differ dy sin2x y+tanx xp Oa None of these Ob sinx…

A: Given differential equation, sin2xdydx=y+tanxdydx-ysin2x=12cos2x If the equation is of the form…

Q: Let 3 sin x + 7 cos y = 3. dy %3D dx d²y dx?

A:

Q: Given that y + x + cos(xy) = 0. Show that dy/dx = ysin(xy)-1 /1-xsin(xy)

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Q: dw If w = x2y sinz - 3zey, find dz 6. O a. dw =x?y cosz - 3exy dz O b. dw =2x2y cosz- exy dz O c. dw…

A: Find the partial derivative of w  with respect to z

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

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Q: Find dy if sin x + 1 = cos y dx²

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Q: find / sin³ x cos³ x dx cos³ 2x sinº 2x dx 11. 12. cos² x dx sin? x dx 13. 14. 16. 7 sin y dy 7 cos'…

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Q: find dy/dx 19) y=Sin" (5x' ) 24) y= Sin 2x.Cos2x 42) y = sinh (tan x)

A: These problems can be solved by the application of Chain rule.

Q: Find the line tangent to f(x) = 3x + cos(8x) at the point wherex-0. %3D Oy-x+1 Oy-x+3 Oy-11x+1…

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Q: Find dy/dx in terms of x and y if cos² (4y) + sin“(4y) = y + 8. %3D

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Q: Evaluate 2.xyz dx + x²zdy +x²ydz over the path r(t) = (t², sin(nt/4), e'“-2') for 0 <t<2.

A: The given integral is: I=∫C 2xyz dx+x2z dy+x2y dzOver the path:  r(t)=t2,  sinπt4,  et2-2t    for…

Q: dy Find ax for y = sinx tanx dy O 1) = cosx tanx + sinx sec2x O 2) dy dx = COSX sinx - sinx tanx %3D…

A: