" hat "(dy)/(dx)=sec^(2)((pi)/(4)+x)

Find (dy)/(dx) , when If y = (cos x + sinx)/(cos x - sinx) , show that (dy)/(dx) = sec^(2) (x + (pi)/(4)) .

A curve y=y(x) is a solution of (x tan((y)/(x))-y sec^(2)((y)/(x)))dx+x sec^(2)((y)/(x))dy=0 passing through the point (1 ,(pi)/(4)) is

if y=tan^(2)((pi x^(2))/(2)), prove that (dy)/(dx)=2 pi x tan((pi x^(2))/(2))sec^(2)((pi x^(2))/(2))

If y=log tan((pi)/(4)+(x)/(2)), show that (dy)/(dx)=sec x. Also find the value of (d^(2)y)/(dx^(2)) at x=(pi)/(4)

If y=sec(tan^(-1)x), then (dy)/(dx)atx=1 is (a) (cos pi)/(4)(b)(sin pi)/(2)(c)(sin pi)/(6)(d)(cos pi)/(3)

If x=a sec^(2)theta and y=a tan^(3) theta, " find " (dy)/(dx)" at " theta=(pi)/(4) .

int_(0)^( pi)(x sec x tan x)/(1+sec^(2)x)dx=(pi^(2))/(4)

if y(x) is satisfy the differential equation (dy)/(dx)=(tan x-y)sec^(2)x and y(0)=0. Then y=(-(pi)/(4)) is equal to

Find (dy)/(dx) , when If y = sqrt((sec x - tanx)/(sec x + tanx)) , show that (dy)/(dx) = sec x (tanx - sec x) .