Let f and g be Differentiable Function Such That f’(x) = 2g(x) And G’(x) = –f(x), And Let T(x) = (f (x))2 – (g(x))2. Then T’(x) Is Equal To

Let [.] denote the greatest integer function and . Then

Let f (x + y) = f (x) f (y) for all x and y. If f (5) = 2 and f’(0) = 3, then f’(5) is equal to

Let f (x) = [x] and

Let

The values of the coefficient a and b for which the function is continuous and has a derivative at x₀, are

Given f’(2) = 6 and f’(1) = 4.  

Let f : R âŸ¶ R be such that f(1) = 3 and f’(1) = 6. Then

The domain of the derivative of the function

If f (0) = 0, f’(0) = 2 then the derivative of  at x = 0 is 

If f is differentiable for all x then 

Let f be a twice differentiable function such that f’’(x) = –f(x) and f’(x) = g(x). If h’(x) = [f(x)]² + [g(x)]², h(1) = 8 and 

h(0) = 2, then h(2) is equal to