Find `(dy)/(dx)` at `x=-1` ,when `(siny)^(sin((pi/2)x))+sqrt3/2 sec^(-1)(2x)+2^x tan(ln(x+2))=0`

Find `(dy)/(dx)` at `x=-1` ,when `(siny)^(sin((pi/2)x))+sqrt3/2 sec^(-

1.	Find `(dy)/(dx)` at `x=-1` ,when `(siny)^(sin((pi/2)x))+sqrt3/2 sec^(-1)(2x)+2^x tan(ln(x+2))=0`
Answer» Correct Answer - `3/(pisqrt(pi^(2)-3)) ` Here, `(siny)^(sin.pi/2x) +sqrt3/2 sec^(-1)(2x)+2^(x) tan {log (x+2)}=0` On differentiating both sides, we get `(sin y)^(sin.pi/2 x)log (sin y)cos.pi/2 xpi/2` `" "+(sin. pi/2x)(sin y)^((sin .pi/2 x)-1)cos y (dy)/(dx) ` `" "+sqrt3/22/((2\|x\|)sqrt(4x^(2)-1))+(2^(x)sec^(2){log (x+2)})/((x+2))` `" "+ 2^(x) log 2 tan {log (x+2)}=0` Putting `(x=- 1, y = - sqrt3/pi)`, we get `(dy)/(dx)=(-sqrt3/pi)^(2)/sqrt(1-(sqrt(3)/pi)^(2))=3/(pisqrt(pi^(2)-3))`