TO/2 ctan x sec x 6. y' cos" xdydx сл /2 psin y Xdxdy 7. [T /1 -x² 8. [[" Jx+y dx dy x+ y

Q: 1. Find y'. y = x² In(tan-1(2x))

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Q: 21. y = sin xy

A: y= sin xydydx=ddxsin xy       =cos xyddxxy       =cos xyxdydx+yddxx       =cos xyxdydx+y       =x…

Q: 7. Let y = tan (3x - 2), find y'.

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Q: 5. Find dªy dx²: y=cscx csc x cotx csc r cot x csc x cot² x - csc x csc x cot² x + csc³ x

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Q: 3. Find the derivative of y with respect to x in the followin u? a) у3 u = 3x' - 2 and u' + 1 b)…

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Q: 2e*/y dy dx 2.

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Q: 5-find Аху : xe 12) if f(x, y) = xe

A: First I have mentioned what we have to find then just use the rule of partial derivative find the…

Q: suppose that y is a differentiable function of x and z = sin (x5y8). Express dz/dx in terms of x,…

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Q: dy for the following implicit functions : dx Find a) x+4xア-ア 5y =3 3べ+5y'x"+4\」 (ans.: 2.x 10xy-y

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Q: x2 sin3(x) Find ax if y = In \cos(x*).V1+x,

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Q: Let y = sin (x + y), find y'.

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Q: Find y' if y = sin² (5+7)

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Q: Q.34. (CotX cosX)/(TT-2x)^3 equals (1) 1/24 (2) 1/16 (3) 1/8 (4) 1/4

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Q: dy – y (xy' -1) .3 2.) dx

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Q: 2. Find dy/dx: a. 3x? – (xy²)½ = 2y³ b. у%3D (сosx — ях)4x*

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Q: 6. x cos x, find the second derivative. 7. y = sin? x, find y dx2 d²y 8. y = tan(3x²), find · dx2"

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Q: 1.Find dy/dx of the following: 5. y = Incose* tan x 6. y = ln(1-xe) 7. y=eta et 4. y= In x 8.…

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Q: e 9. cos(x) dx - " sin(x) dx. Evoluate

A: Formula:∫ cos x dx = sin x + C∫ sin x dx = - cos x + C

Q: x2 – y? + xy = x²y Find dyldx using implicit differentiation.* 2ху-2х-у x-2y-x2 2ху-у x-2y+x² >>…

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Q: Calculate y' given y below. (a) xey = y − 1. (b) y = (cos x)^x (c) y =(√sin^3(√2x))

A: a). Differentiate separately both sides of the equation (treat y as a function of…

Q: Am + bm = S2m = ame™™ + bme¯ L V' 2| dy sin シ (v-) =[V +(-1)"(v' – v)]. тлу L am

A: Here m≠0.

Q: 21. y = csc 2x 22. y = tan 2 Vx* + 1 x tan x 24. y 23. у x? + 1 1 + sin? x

A: