f(x)=(x+1)^(3)(x-3)^(3)

If f(x)=tan^(-1)((3x-x^(3))/(1-3x^(2))) then (d)/(dx)(f(x)) is equal to

If f(x)=tan^(-1)((3x-x^(3))/(1-3x^(2))) and phi(x)=cos^(-1)((1-x^(2))/(1+x^(2))) , then the value of lim_(x to a) (f(x)-f(a))/(phi(x)-phi(a))(0 lt a lt (1)/(2)) is -

If f(x)=cot^(-1)((3x-x^(3))/(1-3x^(2))) and g(x)=cos^(-1)((1-x^(2))/(1+x^(2))) then lim_(x rarr a)(f(x)-f(a))/(g(x)-g(a))

If f(x)= x^(3)- (1)/(x^(3)) then show that f(x)+ f((1)/(x))= 0

If f(x)=x^(3)+(1)/(x^(3)), then f(x)+f((1)/(x)) is equal to

If f(x)=x^(3)-(1)/(x^(3)) show that f(x)+f((1)/(x))=0

If f(x)=x^(3)-(1)/(x^(3)), show that f(x)+f((1)/(x))=0

If f:RrarrR be given by f(x)=(3-x^(3))^(1//3) , then f^(-1)(x) equals:

f(x) =3x +(1)/(3x)

Find the inverse of the following functions(i) f(x)=sin^(-1)((x)/(3))x in[-3,3]