If #x=sint# and #y=cost#, then #(d^2y)/dx^2# = ?

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Answer 1 · 2017-12-17T12:28:30

The answer is #=-sec^3t#

#x=sint#

#y=cost#

First calculate the first derivative

#dx/dt=cost#

#dy/dt=-sint#

#dy/dx=-sint/cost=-tant#

To find second derivative

#(d^2y)/dx^2=(d/dt(dy/dx))/(dx/dt)=(-sec^2t)/(cost)#

#=-sec^3t#