IIT JEE , AIEEE Forum - Mathematics , Differential Calculus

sparkz

y = logcosxsinx x (logsinx cosx)^-1+sin^-1 2x/(1+x²)

so [dy/dx] at x= pie/4 is ??

sparkz

is there any one??

johri_anshuman

y = logcosxsinx x (logsinx cosx)^-1+sin^-1 2x/(1+x²)

=>y= 2log (sinx)/log (cosx) + sin^-1 2x/(1+x²)

let u=2log (sinx)/log (cosx)
du/dx = 2[ cosx log (cosx)/sinx + sinx log(sinx)/cosx]/(log(cosx))²

v=sin^-1 2x/(1+x²)
put x=tan@

v=sin^-1(sin2@)

v=2@
=>v=2tan^-1x
=>dv/dx=2/1+x²

dy/dx=du/dx+dv/dx
=> dy/dx=2[ cosx log (cosx)/sinx + sinx log(sinx)/cosx]/(log(cosx))² + 2/1+x²

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