Find the first derivative of the following: 1. y= y = Ine-tanh² 2x 2. Y= sech(5x-1)tanh(5x-1) 3. Using logarithmic differentiation find y' for xy= 5 x (5x-2) 4. y= e-Inx? cos2x

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A: Solution is given below:

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A: As per our guidelines I am solving only first problem please repost other question.  y = sinh(x).…

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A: Introduction: The four-step method to find derivatives is actually determining the derivative of a…

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A: The given function to be derivated is,

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A: Formula used: ddx[u(x)v(x)]= u(x)v(x).ddx[ln(u(x)).v(x)] ddx(u.v) =dudx.v + udvdx

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A: Product Rule of Differentiation : d(u.v)dx = u.dvdx+dudx.v

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A: 1.) x²y + y²x = -2    2.) √(xy) = x²y+1 ntiderivatives for integral notation. (x+7) dx

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A: We first expand the equation using the addition property of log and the change of base property.

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A: Topic  =Derivative

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Q: 3. Find the derivative of: y = csch¬(In (sech(sec()))).

A: Note:Two questions submitted simultaneously, kindly upload question 2 separately.

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A: Implicit differentiation

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