`1/(sqrt(x+a)-sqrt(x+b))+x^2sin(x^3)`

Find the derivatives w.r.t. x : (1)/(sqrt(x+a)-sqrt(x+b))+x^(2)sin(x^(3))

f(x)=(1/sqrt(b-a))(((sqrt((b-a)/a))sin2x)/sqrt(1+((sqrt(b-a)/a))sinx)^2)(sqrt(a+btan^2x) at x=3pi/4

f(x)=(1/sqrt(b-a))(((sqrt((b-a)/a))sin2x)/sqrt(1+((sqrt((b-a)/a))sinx)^2))(sqrt(a+btan^2x)) at x=(3pi)/4

intsqrt(x/(1-x))\ dx is equal to (a) sin^(-1)sqrt(x)+C (b) sin^(-1){sqrt(x)-sqrt(x(1-x))}+C (c) sin^(-1){sqrt(x(1-x))}+C (d) sin^(-1)sqrt(x)-sqrt(x(1-x))+C

Applying logrithmic differentiation find the derivatives of the following functions (a) y=(cos x)^(sin x) (b) y=((3 sqrt(sin 3x))/(1-sin 3x)) (c ) y=sqrt(x-1)/((3sqrt(x+2))^(2)(sqrt(x+3))^(3))

int_(0)^(1)sin^(-1)(x sqrt(1-x)-sqrt(x)sqrt(1-x^(2)))dx

(1)/(sqrt(x)+sqrt(x+1))+(1)/(sqrt(x+1)+sqrt(x+2))+(1)/(sqrt(x+2)+sqrt(x+3))+...(1)/(sqrt(x+98)+sqrt(x+99))

sin^(-1)[sqrt(x^(2)-x^(3))-sqrt(x-x^(3))]=..... a) sin^(-1)x+sin^(-1)sqrt(x) b) sin^(-1)x-sin^(-1)sqrt(x) c) sin^(-1)sqrt(x)-sin^(-1)x d) 2sin^(-1)x

int sqrt((x)/(1-x))dx is equal to sin^(-1)sqrt(x)+C(b)sin^(-1){sqrt(x)-sqrt(x(1-x))}+C(c)sin^(-1){sqrt(x(1-x)}+C(d))sin^(-1)sqrt(x)-sqrt(x(1-x))+C

f(x)=((1)/(sqrt(b-a)))(((sqrt((b-a)/(a)))sin2x)/(sqrt(1+(((sqrt(b-a))/(a)))sin x)))(sqrt(a+b tan^(2)x) at x=3(pi)/(4)(sqrt(a+b tan^(2)x)