Question

Find d^2y/dx^2(independent of t) of the function x= sin(lnt) and y=cos(lnt)

Answer 1

Answer:

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Answer 2

x = sin(lnt)

dx/dt = cos(lnt) * 1/t = y/t

y = cos(lnt)

dy/dt = -sin(lnt) * 1/t = -x/t

so, dy/dx = -x/y

hence, d^2y/dx^2 = -(y - xdy/dx)/y^2

= -(y - x* -x/y)/y^2

= -(y^2 - x^2)/y^3