fG) = sin h e2y : find f'(y) f'G) = e2y cot hezy O None of the above. O Option 4 f'6) = e> coshe f'G) = 2 e²» coth e²y O Option 3 O Option 2

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A: 13) Given

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Q: =記 う f6)2iぜsintdt b) f(x) = j sint? dt

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Q: f(1,-2,リミ

A: using substitution

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Q: critical ininibers f have? Itow many does hee 2. f'Cx) = 100 cos-L) %3D 2. 10tx

A: Given that: f'(x)=100cos2x10+x2-1

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A: given function :y= cotx+(cotx)lnsinx

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A: our objective is to find the derivative and tangent line

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A: Given : y = xsinx,     at  x=π2

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A: The given function is: y=sin(ax)cos(bx) So, y'=sin(ax)ddx(cos bx)+cos(bx)ddx(sin(ax))…

Q: Find the derivative of y. 30) y- In (sinh 9x) 1. B) sinh 9x A) coth 9x C) 9 csch 9x D) 9 coth 9x

A: Derivative

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A: To prove: d(tan u)/dx = sec2u (du/dx)

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Q: fi fa>= 2 g. %3D 4X+1 3X-2 he fの= Wi fac) = X²+1 X3+1

A: There are multiple sub parts, As per company Policy I have answered first 3 subparts g.

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A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…

Q: Find the directional derivative of fix, y) = sin(y) at the point P (1.5) in the direction

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Q: 1) Determine the derivative o a) f(x) = -4e*² b) y = cos(3*) c) g(x) = -2 sin3 (2x) %3D %3D

A: Note: Multiple subparts are given, we are answered with first three parts only, if you need more…