Defferentinate `y=sin(x^(2))`

y=x^(sin2x)

solution of the differential equation (x^(2)sin^(3)y-y^(2)cos x)dx+(x^(3)cos y sin^(2)y-2y sin x)dy=0 is

the value of lim_(x rarr y)(sin^(2)x-sin^(2)y)/(x^(2)-y^(2)) equals

Solution of differential equation (2x cos y + y ^ (2) cos x) dx (2y sin xx ^ (2) sin y) dx = 0 is (a) x ^ (2) cos y + y ^ (2) sin x = C (b) x cos yy sin x = C (c) x ^ (2) cos ^ (2) y + y ^ (2) sin ^ (2) x = C (d) x cos y + y sin x = C

Draw the graph of y=sin x and y=sin . (x)/(2) .

If x + y = pi + z, then prove that sin ^ (2) x + sin ^ (2) y-sin ^ (2) z = 2sin x sin y cos z

Sketch the graphs of the following function: (i) y=2 sin x (ii) y=3 "sin"(x+1) (iii) y="sin"(x)/(2)

If y=x sin(a+y), prove that (dy)/(dx)=(sin^(2)(a+y))/(sin(a+y)-y cos(a+y))

Prove the following Identities (sin(x+y)-2sinx+sin(x-y))/(cos(x+y)-2cosx+cos(x-y))=tanx

If x sin(a+y)+sin a cos(a+y)=0, prove that (dy)/(dx)=(sin^(2)(a+y))/(sin a)