up To nterms, Then y’(0) Is Equal To

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 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

If y² = P(x) is a polynomial of degree 3, then    

              is equal to  

If  then the set of all points where the derivative exist is

The value of y’’ (1) if x³ – 2x²y² + 5x + y – 5 = 0 when y(1) = 1, is equal to

If f(x) , then f’(1) equals     

If f (x) = (1 + x)ⁿ, then the value of  

The solution set of f’(x) > g’(x) where f(x) = (1/2)5^{2x + 1} and g(x) = 5^x + 4x log 5 is  

Let f(x) = sin x; g(x) = x² and h(x) = log x.  

Let f and g be functions satisfying f(x) = e^x g(x), f (x + y) = f (x) + f(y),g(0) = 0, g’(0) = 4 g and g’ are continuous at 0.  

Then