`2x (3x+3x)=`

Simplify: 2x^2(x^3-x)-3x(x^4+2x)-2(x^4-3x^2)

|[1,1,1] , [(2^x+2^(-x))^2, (3^x+3^(-x))^2, (5^x+5^(-x))^2] , [(2^x-2^(-x))^2, (3^x-3^(-x))^2, (5^x-5^(-x))^2]|=

Differentiate the following functions w.r.t. x. (2x +3) (x^3 - x+ 2)

Let tan^(-1)y=tan^(-1)x+tan^(-1)((2x)/(1-x^2)) , where |x|<1/(sqrt(3)) . Then a value of y is : (1) (3x-x^3)/(1-3x^2) (2) (3x+x^3)/(1-3x^2) (3) (3x-x^3)/(1+3x^2) (4) (3x+x^3)/(1+3x^2)

If f(x) = 1/2 (3^x + 3^(-x)), g(x) = 1/2 (3^x - 3^(-x)) , then f(x) \ g(y)+f(y) \ g(x)=

The series . (2x)/(x + 3) + ((2x)/(x + 3))^(2) + ((2x)/(x + 3))^(3) + ...oo have a definite sum when

Which of the following experessions is equivalent to the expression given below ? (2x ^3 -x-1)-3(x^4+2x^3-2x^2-x-3)

Find the derivative of f(x) = 2 x^(3) + 3x^(2) + 5x + 9 at x = 2

The interval in which the function f(x) = 2 x^(3)+ 3x^(2) - 12 x + 1 is xtrictly increasing is