dy B) Find for all the following dx 1) y = sin-13x 2) y = In(5x) 3) y = Vtanhx

Q: . If y = tan( sin t (. cos t-1 1 dy %3D show that dt 2

A: The given details are as follows. y=tan-1sin tcos t -1 Observe the chain rule of differentiation as…

Q: Suppose that y = 4 cos² t , x = v3 sin(2t) and 0 < t<a. Then dt2

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Q: 7. Find the dy/dx of * y = In sin 5x

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Q: If y = (2x)sin (4z) , then dy sin(4æ) · (2sin(4z) esin(4z) In(x)) %3D dx X synta

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Q: Find dy/dx for y = (cos x) 2 + sin(x 2 )

A: Given that      y = (cos x)2 + sin(x2) We have to find dy/dx .

Q: Find dy/dx of y = cos^-1(2x) * sin^-1(2x)

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Q: If Sin-'x= Iny, show %3D ( l-xx) day - dx d X 2 x dy =y

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Q: If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] True or False.

A: Given statement If y=sin-1x then dy/dx= 1/dx/dy for all x in [-1,1] is false.

Q: √xA)• dS over the surface of a hemispherical bowl of radius 2 and its circular rim if A = 3 sin(-)â,

A: Please see the attachment

Q: 29. [sin (9y)sec (9y)dy

A: Use the formula sin2x + cos2x =1.

Q: Let 5 sin æ + 6 cos y = 6. dy dx d?y dx?

A: 5 sinx +6 cosy = 6  Differentiating w.r.t x,  5 cosx +6 (-siny) dy/dx = 0  dy/dx = 5cosx/(6siny)

Q: If given integrand is x² cos 2x dx and dv is equal to cos 2x dx, what is v?

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Q: z = sin(6x) sin(5y) az az dy II

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Q: 3y dx 2 (2y In +3 sin y]dy =- + 3 Sin Y X+ 3

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Q: Compute dy/dx if sin(x) = cos(xy^2

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Q: 10. Find , if y = dy 1-cosx dx 1+cosx

A: Given  y = (1- cosx) /(1 +cosx) To find dy/dx

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

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Q: F(x, y, z) = (6x° sin(y) + cos(18z), xº cos(y), – 18x sin(18z) + 6z°)

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Q: 3. Integrate the following dx (i) V9 – x² (ii) ſe-3*cos4x dx (iii) ſ sin³2x dx -

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Q: 1od of undc cients, obtain the general y" – 2y' – 3y = 2 sinx

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Q: Q1: show that 1) d/dz [cosz] = -sin z, * 2) 1+tan2 z = sec2 z

A: 1) ddz(cos z)=-sinz2) 1+tan2z=sec2z Results:ddxf(x)=limh→0f(x+h)-f(x)hlimx→0sinxx=1limx→01-cosxx=0

Q: 2. if 2x3 +10 x?siny-y"tanx = 0 ノ the y' so dy write ex pressin in terms of X and y.

A: Applying implicit derivative we have

Q: 1) ſ y³ sin(2y) dy

A: As per our guidelines we are supposed to answer one question , kindly repost the remaining questions…

Q: 2.Find , if y = sinh x %3D dx' 1+cosh x

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Q: 2. Integrate using Trig: cos° x dx

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Q: 23, zax + sec(x)cos(y) 0, y(0) = 0

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Q: 19. i) Differentiate sinx with respect to x from first principle 1+3x dy ii) Find, dx when a) y (x…

A: Part i,Given,          fx=sinx

Q: 2. Show that the LT of sin(wt) is L sin(wt)] (s) where w is a positive constant.

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Q: 4. Ify =/sin x+ /sin x+.to inf inity, dy _ cosx dx 2y-1 prove that

A: Derivative of Sinx is Cosx

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: Integrate (three) of th 1) f sin6x cos3x dx 4) [x² (1+¹)4 dx

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Q: 2.1 Given that 1 sinh x show that dy cosh a. dx

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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: dy 1. sin 2ycos2y

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Q: Integrate by parts f(x)=sin4(x)cos3 (x) dx

A: Given the integral  I = ∫cos3(x) sin4(x) dx cos2(x)=1−sin2(x) I = =∫cos(x)(−sin4(x)(sin2(x)−1)) dx…

Q: sin³€ dt to ylomeldon 3.

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Q: 4) S tanx dx cosxv1+secx 5) S(1- u)Vūdu

A: (4)  First we integrate this ∫tanxcosx1+secxdx

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: y = In(x +1)

A: Given that : y = ln(x2 + 1). Find dy/dx  We know that derivative of - d(lnx)/dx = 1/x. And d(xn)/dx=…

Q: 5. Integrate: S (cose-sin8) de sec 20 6. Find f(3y – y³)ž(1 – y?)dy

A: 5. Given integral, ∫ecosθ-sinθ2sec2θ

Q: S cos(2x + 1) sin(3 – 4x)dx

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Q: 7 Find (b) x siny-ycosx-y = 1. dx

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Q: 7 Show that: sech x dx = Sin¹ (tankx) + ( S note: * & Sim'u = dx 1-U² dx Cam multiply sechx by * you…

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Q: on the right. Prompts Submitted Answers D Ssin(3x)sin(4x)dx S(cos(x) - cos(7x)dx} Jsin(3x)cos(4x)dx…

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Q: Find dy/dx if y = In (tan(x).3$ec(x) + /sin (x³)

A: given,