1. Differentiate each of the following with respect to x (find y' =2). Do not simplify your answers past the point of %3D dx getting them to the form y'= a) y = (3e* + 4x2)* b) y = 8*+tanx 3x²+4x+2 c) y = d) sin(xy) x-y

Q: 1. Find y'. y = x² In(tan-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: Find of an

A: We are asked to find y'

Q: 2x fe²x sinx dx

A: Using integration by part.

Q: (a) [- 9x2 +x° cos x dx = 3

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: 1. Calculate an expression for = y if V+b°y = tan-(x"y)

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Q: 3. S sin x sec®x dx

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Q: y = π/2 sinx y' =

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Q: Find y' if y = sin² (5+7)

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Q: @ y = x tan 2x

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Q: 1. sin° x cos x dx

A: sin3x cos4x  = sin(x) sin2(x) cos4(x)  = sin(x) (1 - cos2(x)) cos4(x)  = sin(x) (cos4(x) - cos6(x))…

Q: 3 sin x 1. S- dx 1+cosx

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Q: Sr12 (sin 2x)(ecos2x)dx π/2

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Q: 13. (D -1)y = x' sin 3.x

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Q: 4) If y = 2√x - 2 tan-¹ √x, then y y' = -1 1+x²

A: Given :y=2x-2tan-1x

Q: Find d²y/dx² if y = =x cos(3x) — sin²(x). -

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Q: 4 sin' 2x cos 4x dx 4.

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Q: Given f''(T) 9 sin(3r) and f'(0) 6 and f(0) = 3. Find f 2.

A: Given f"(x)=-9sin(3x) and f'(0)=-6 and f(0)=3

Q: 2e3* sin 2x dx

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Q: 3. S sin? (2t) cos³ (2t) dt 4. ſ tan³(3x)dx

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Q: Find y' and y". y = cos(x?) y' - -sin (x²) ( 2x) y" =

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