Question

If `x = e^(sin^-1t),y=e^(cos^-1t)`

find `dy/dx  "at"  "t"=1/sqrt2`

Answer 1

`xy = e^(sin^-1t)xxe^(cos^-1t)`

`xy=e^(sin^-1t  +  cos^-1t)`

`xy=e^(pi/2)`

⇒ `xdy/dx+y(1)=0`

⇒ `dy/dx=(-y)/x`

= `-e^(sin^-1t)/e^(cos^-1t)`

= `(-e^(pi/4))/(e^(pi/4))`

= –1