Which Of The Following Functions Is Differentiable At x = 0?

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.  

 up to nterms, then y’(0) is equal to

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

Let f : R → R is a function which is defined by f (x) = max {x, x³}. The set of all points on which f (x) is not differentiable is

If f is a differentiable function at a point ‘a’ and f’(a) ≠ 0 then which of the following is true.