Statement 1: Both `sinxa n dcosx` are decreasing functions in `(pi/2,pi)` Statement 2: If a differentiable function decreases in an interval `(a , b),` then its derivative also decreases in `(a , b)` .

Consider the following statements in S and R S: Both sinx and cosx are decrerasing function in the interval (pi/2,pi) R: If a differentiable function decreases in an interval (a,b), then its derivative also decrease in (a,b).Which of the following it true? (a) Both S and R are wrong. (b) Both S and R are correct, but R is not the correct explanation of S. (c) S is correct and R is the correct explanation for S. (d) S is correct and R is wrong.

Statement-1: The function f(x)\ =\ ln\ x is increasing in (0,10) and g(x) = 1/x is decreasing in (0,10) Statement-2: If a differentiable function increases in the interval (a , b) then its derivative function decreases in the interval (a , b) .

The function f(x) = x^x decrease on the interval

The function x^4-4x is decreasing in the interval

Show that f(x)=cos^(2)x is a decreasing function on (0,pi/2)

Show that f(x)=cos^(2)x is decreasing function on (0,(pi)/(2))

The function f(x)=tan^(-1)x-x decreases in the interval

The function f(x)=tan^(-1)x-x decreases in the interval.