[y=cos^(-1)(sqrt((1+x)/(2)))(d)/(dx)=?],[" (b) "x=cos theta=0=cos^(2)x]

If int sqrt(1+sec x)dx=2sin^(-1)[sqrt(2)f(x)]+c then (d)/(dx)[f(x)] is equal to (A)cos(x)/(2)(B)-(1)/(2)cos(x)/(2)(C)(1)/(2)cos(x)/(2)(D)(1)/(2)sin(x)/(2)

(d)/(dx)[cos^(-1)(x sqrt(x)-sqrt((1-x)(1-x^(2))))]=(1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(-1)/(sqrt(1-x^(2)))-(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))+(1)/(2sqrt(x-x^(2)))(1)/(sqrt(1-x^(2)))0 b.1/4c.-1/4d none of these

(d)/(dx){sin^(-1)(e^(x))} is equal to (a) e^(x)sin^(-1)(e^(x)) (b) (e^(x))/(sqrt(1-e^(2x))) (c) (e^(x))/(1-e^(x)) (d) e^(x)cos^(-1)x]]

d/(dx)(sin^(-1)x+cos^(-1)x) is equal to : (A) (1)/(sqrt(1-x^(2))), (B) (2)/(sqrt(1-x^(2))), (C) 0 (D) sqrt(1-x^(2))

d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) (-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2))+1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2)) 0 b. 1//4 c. -1//4 d. none of these

d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) (-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2))+1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2)) 0 b. 1//4 c. -1//4 d. none of these

d/(dx)[cos^(-1)(xsqrt(x)-sqrt((1-x)(1-x^2)))]= 1/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) (-1)/(sqrt(1-x^2))-1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2))+1/(2sqrt(x-x^2)) 1/(sqrt(1-x^2)) 0 b. 1//4 c. -1//4 d. none of these

2cos theta=x+(1)/(x) and 2cos phi=y+(1)/(y) then (A)x^(n)+(1)/(x^(n))=2cos(n theta)n in Z(B)(x)/(y)+(y)/(x)=2cos(theta-phi)(C)xy+(1)/(Xy)=2cos(theta+phi)(D)x^(m)y^(n)+(1)/(x^(m)y^(n))=2(cos m theta+n phi),m,n in Z

The solution of the differential equation (x^(2)dy)/(dx)cos((1)/(x))-y sin((1)/(x))=-1, where y rarr las x rarr oo is (A) y=sin((1)/(x))+cos((1)/(x))(B)y=(x+1)/(x sin((1)/(x))) (C) y=sin((1)/(x))-cos((1)/(x))(D)y=(x)/(x cos((1)/(x)))