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If x = 3 tant and y = 3 sec t, then the ...

If x = 3 tant and y = 3 sec t, then the value of `(d^2y)/(dx^2)" at" t=pi/4` is

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The correct Answer is:
6
`x=3tant" "therefore" "y=3sect`
`y^(2)-x^(2)=9`
`2yy'-2x=0`
`y'=(x)/(y)`
`y'=(y-xy')/((y)^(2))`
`y'|_(t=(pi)/(4))=(3tan((pi)/(4)))/(3 sec((pi)/(4)))=(1)/(sqrt2),x=3, y=3sqrt2`
`y''=(3sqrt2-3sqrt2)/(18)=(3)/(18sqrt2)=(1)/(6sqrt2)`
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