Differentiate: y = cot(xcsca) = cot x (xcsca - 1) csc (zcsca) Oy = cot x (xcscx +1) csc (xcscx) = csc x (xcotx +1) csc2 (xcscx) Oy = csc x (1– xcotx) csc (xcscx) oy = cot a (1 – xcsca) csc (xcscz) Oy = cscx (rcotx - 1) csc (xcscx)

Q: (cos x cos y cotx) dx - sin x sin y dy = 0. -

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Q: sec" y dy- (f) tan y

A: Topic = Integration

Q: use implicit differentiation to find dy/dxin terms of x and y .

A: We have to find implicit derivative (dy/dx) of the curve .Information is given below:

Q: Find fyyzz if f(x, y, 2) = cos(3y + az). Then evaluate fygazz at point (, 0, 4). COS

A: *Use chain rule

Q: Find the absolute maximum and minimum values for f (x, y) = 5 sin(x) + 9 cos(y) on the rectangle R…

A: Given that, fx,y=5sinx+9cosy where, 0≤x≤2π and 0≤y≤2π. Calculate the values of absolute maximum and…

Q: Find the minimum value of ∣sin x + cos x + tan x + cot x + sec x + csc x∣ for real numbers x.

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Q: Find the curve y(x) that minimizes the I Cy) = S. cos x)+ ]2 Cunc tonal %3D

A: solution:-Given I=∫1+cosx+y121/2using Euler's equation ∂f∂y-ddx∂f∂y'=0sincef=1+cosx+y121/2is…

Q: Find all points (if any) of horizontal and vertical tangency to the curve on the given interval

A: Given Data The first equation is x=cos θ+ θ sin θ. The second equation is y=sin θ- θ cos θ.…

Q: f(x) = cotx-secX %3D %3D COSX

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Q: 5. In rectangular coordinates verify that V · V x A = 0 where A = xyz(ê+ ŷ + 2) by carrying out the…

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Q: Prove that (arccsc x) dx d d %3D (csc-1 x) = %3D - dx Ju/Vu2-1

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Q: luaté the lntegr sec2 x Vtan x xp= sec x . tanх + С 2ysec x + C 2/tan x + C

A: We will use substitution method to find the integral of given expression.

Q: Differentiate: y = arcsin + Oy = y = - 4-x O y = x V4 – x2 4-x2

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Q: a) cot x – tan x sec x(csc x – 2sinx) %3D b) cor y(sec²y – 1) = 1

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Q: y tan -- arccos y

A: In this question, we need to check whether the given function is homogeneous or not and the degree…

Q: (2x + 3) csc²() dx + f 4 tan () dx = 2(2x + 3) cot (#) f(2x + 3) sec² () dx - 4 tan ) dx = 2(2x + 3)…

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Q: 6- y" + 4y = cot(t)

A: Given:        y''+4y=cott        4yt+d2dt2yt=cott The differential has the form        y''+py'+qy=s…

Q: tan°(x) sec²(x) dx = 1/7tan^7(x)+1/9tan^9(x) %3D

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Q: Differentiate y = arcsin(2x + 1) y’

A: Given data: The given expression is y=arcsin(2x+1). The expression for the differentiation of the…

Q: 4. The 1" derivative of y : cotx a) xsec?x + tanx b) xsecx - tanx c) cot x + xcsc'x d) cot x - xcscx

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Q: Find dyldx y =-secu, u = x- COs X dy -sin(x-cos x) cos x) sin(x-cos x) cos(x - cos x) sec(x- %3D dx…

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Q: ‚arcsin(1+x²)] y'of y = In cscya

A: Given y=lnearcsin1+x2cscxWe need to find y'

Q: 1) y = Arcsin(1 – x²) 2) y = Arctan Vx² + 2x 3) y = Arctan /t²-1 + Arccsc t

A: Given : 1) y = Arcsin (1 - x²) 2) y = Arctan (√x² + 2x) 3) y = Arctan (√t² -1) + Arccsc t

Q: Use differentiation rules to find y' = dy/dx.

A: To determine the derivative of the function.

Q: (cos x cos y cotx) dx - sin x sin y dy = 0 -

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Q: Evaluate limy-0 sin3y cot 5y y cot 4y

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Q: Solve the problem using partial differentiation A metal cube (faces 20 mm ±0,1 mm) TI

A: volume of metal = volume of water rise

Q: siny dle = (1-x cosy) Cas y

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Q: d -tan(z) = dz sec(x) O cot(x) O sec2(z) O

A: we have to find ddztanZ i.e we have to find derivative of Tanz with respect to z ddzTanz=sec2zdzdz

Q: cos(etan 3x) y cos

A: The given function y=cosetan3x

Q: A cable hangs between two poles of equal height and 24 feet apart. Set up a coordinate system where…

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Q: Integrate f(cos x)e*+sin xdx B. e-sinx +C A. -et+sinx + C c. ettsinx + C D. e+sinx C

A: Note:∘ddx(sinx) = cosx ∘ddx(a) = 0                                         where a is constant∘∫etdt…

Q: ldx on the graph y sec x? + y? = cos2x at point (1, 2).

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Q: Find the partial derivative. z = sin (6

A: We have to find

Q: (c) curve y = 5-x", line y=x+3 (d) y= sinx, y=cosx, x= 7 /4, x=7/2

A: Double integers

Q: Cos ly -A) %3D show that 2 ニ0 2 8x Sx8y

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Q: EVaLuateAt W= X X=cos't Y=cost sin

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Q: f(x) = cos x + 3, [0, 27], midpoint

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Q: find 3 sec“ 3x dx sec4 0 do 41. 42. csc“ 0 do secó x dx 43. 44. 7/4 4 tan³ x dx 6 tan“ x dx 45. 46.…

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Q: Q3|A: Find ý if 1-y = cot vx +2 2- y = tan v+ Vtan x 3- y = tan x+ * cot v

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Q: [10] Find y' of arcsin x/y + arccos y/x = 1

A: Differences

Q: y = Arccot (cosx ) ; y' ' O sin x/ (1+ sin*2 (x) ) ) - sin x / (1+ sin^2 (x) ) ) sin x/ sqrt (1-…

A: Given y=cot-1cosx We will find y'that is the derivative of y. Chain Rule: If y=fgx, then y'=f'gx·g'x

Q: 10. f cos*x sin x dx 11. (sec² 3x) dx / (tan 3x) 12. Setan 2x sec² 2x dx

A: Topic:- integration  Note:- as per our guideline if more than three subparts posted than only first…

Q: 2cscx 1.) %3D 1-COSY £) tanx t cot x = secx cs CX %3D a.) 1-sinx = (SECX – tanx)* Itsinx %3D

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Q: Use differentiation rules to find y′=dy/dx   y = 3 · cos5 ( x − 4/x2 )

A: We apply the power rule then apply the chain rule

Q: cos y sin x Let f(x.y) x+0 %3D cos y x=0 Is continuous at (0, 0) ?

A: Continuity

Q: 1- x 30. y= arctan V %3D 1+x

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Q: Differentiate. y = 3x2 cos x cot x y' = 6x cos (x)cot(x) + 3x2.-sin(x)cot(x)· csc2(x)

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