5. y = l 1- co s x 1+co s x

Q: Find dy/dx for the following : 1) y = x3 + sin x² + sin-1 5x 2) y = 32x + In (sin x²) + In(sin-1 5x)…

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Q: Find for the following function: dx 1- y = sin-1 V2x + 3 2- y = 3cot(cosx) 3- y = x*y at x = 1

A: We have to find the derivative of the following functions.

Q: B. By miscellaneous substitution (VE+1)dx dx 1. S 2. S: 3 cos x+2 sin x-5 XA +

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Q: If x = tan - log y a d'y dy Show that (1+x²)- +(2x- a)-0 dx dx?

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Q: use the chain rule to find: 28) dv 2- COSxy + y cos x

A: Solution:Given   z= cos xy+ y cos xx=u2+v and y=u-v2To find :dzdvFormula:ddx(cos x)=-sin…

Q: dy соmpute dx for implicitly given function cos(xy) + 2y = x³

A: cos(xy)+2y=x3Differentiate with respect to x,-(sin(xy))y+xddx(y)+2ddxy=3x2

Q: dy Determine the general solution of = 1+ 3y tanx. dx

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Q: xdx x²+6x+18 7. f cos(lnx)dx 8. fest sin(at) dt 6. f

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Q: Q1\| Integrate SIX of the following functions: sinh(lnx)dx 1) 3) | sin?(2x).cos(3x) dx 2) ex. sinxdx

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Q: Se* sin e*dx

A: We have to find integrating of given Questions

Q: find dy/dx. y = -10x + 3 cos x

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Q: Solve dx dy for y= sec (In x) In (tan x)

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Q: Ho Find (dy/dx) for: tanh-¹(x y) + e(x+y) 5 cos(y)

A: It is given that, tanh-1xy+ex+y=5cosy. The objective is to find dydx. Formulas used:…

Q: Find the local linear approximation of cos x at xo = cos 61°. T/3 and use it to approximate

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Q: dy Find for three only: dx 1) y = In(cos x . Inx²)

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Q: Solve th D.E using Exact dx +(x² +3y* )dy

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Q: Find dy/dx for following functions. 1) y = csc-(e2lnx) + sin-1(2lnv3x)

A: it is given that,  y=csc-1e2lnx2+sin-1(2ln3x) we have to find dydx=?

Q: 211 sin nx dx [ [1-cos2nx]dx t, where n %3D

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Q: Simplify (if necessary) then Compute: y" +y' for [6(cosh2x- sinh2x)] d -3x2 dx a2 y(z) = [; (z²x+…

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Q: Find dy/dx of y=sin-!x+cos -!x dy/dx is Blank 1.

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Q: dy Find dx if y = cos (4x - 3x + 1) s*(4x²-3x + 1)

A: Given that, y=cos4(4x2-3x+1)

Q: find dy/dx where y=sin^3x+cos^6x

A: Given:

Q: 1. Find dy for the following functions : dx Vsin x.cos x 1+2.ln x 3y (ans.: coi x 2 tan x -)) x(1+2…

A: To solve given differentiation easily we take logarithm on both sides and then differentiate it.

Q: Find dy/dx: y = sin (In x²). A 2 cos (In x²) (B) 2 cos (In x²) / x

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Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x*+1) 3- xy + x²y = 3 at x = 1 4-…

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Q: Find dy for y = ln dx ² cosx %3D sec x

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Q: Find dy/dx by implicit differentiation cos(x) sin(y) = x2 − 3y

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Q: Find dy/dx for following functions. 1) y = csc-(e2inx?) + sin-1(2lnv3x)

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Q: dy/dx of y=cos^-1 (e^-3x)

A: Given y=cos-1e-3x

Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

A: Here we can use the following formula  If z=fx,y, thendz=fx dx+fy dyδzδy=fx δxδy+fy

Q: find dy/dx. y = x2 cos x - 2x sin x - 2 cos x

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Q: Find dy/dx of y=sin -1(1/x). (A x²– 1 3 B 1- 9x2 1 9 D 1-x2

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Q: Find dy/dx of the function below. 2x³ + e^(2y) = cos3y

A: 2x3+e2y=cos(3y)Differentiate with respect to…

Q: find dy/dx. g(x) = cos x/sin2 x

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Q: find dy/dx. ƒ(x) = x3 sin x cos x

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Q: Find . dy dx e 4x, = sin (x + 8y) %3D O In sin (x + 8y) 4e4x -1 S cos (x + Sv) S cos (x + Sv) 4ex -…

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Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x+1) 3- xy + xy = 3 at x = 1 4- y…

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Q: Find dx (e3t + 1)dt. -cos(3rx)

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Q: dy of y = sin(3x² + 5x – 4) * In(e*) is dx

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Q: Find dy/dx by implicit differentiation. (sin mx + cos my)4 = 74 dy/dx=

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Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x+1) 3- xy + x²y 3 at x = 1

A: Here, We need to find the derivative of the given functions. To solve these questions, we need chain…

Q: Find dy of the function y = cos2 3X + √√Sin x dx

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Q: Use the trapezoidal rule withn= 4 to approximate cos(x) dx Keep at least 2 decimal places accuracy…

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Q: Find dy/dx implicitly. exy + x2 - y? = 11 |

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Q: Find dy/dx by implicit differentiation y cos x = 2x? + 5y2

A: Given,           ycosx=2x2+5y2

Q: Find dy/dx for the following : 1) y = x + sin x² + stn-! 5x 2) y = 32x + In (stn x²) + In(sin-1 5x)…

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Q: dx y of y = dy cos-1(ln (xy)) Find

A: We write cos-1 as acos for simplicity. The derivative is too complex. So, we take the help of an…

Q: Show that d/dx(ln kx) = d/dx(ln x), where x > 0 and k is a positivereal number

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Q: Find (dy)/(dx) if ey = ex + sin(x2x).

A: Given ey=ex+sinx2x

Q: 3 dy Find dx if y = cos vx + 4sin x – log 3(3x + 1)ž. إضافة ملف

A: We will solve the following