If $f(x)$ is an even function and $f^{\prime}(x)$ exists,then $f^{\prime}(e) + f^{\prime}(-e)$ is

If $y = (1 + x^{1/4})(1 + x^{1/2})(1 - x^{1/4})$,then $\frac{dy}{dx} = $

Let $f(x) = x^3 + x^2 f'(1) + x f''(2) + f'''(3)$,where $x \in R$. Then $f'(10)$ is equal to:

Let $f$ be a differentiable function such that $f(1) = 2$ and $f'(x) = f(x)$ for all $x \in R$. If $h(x) = f(f(x))$,then $h'(1)$ is equal to

The differential coefficient of $\sec^{-1} x$ is:

Let $f(x)$ and $g(x)$ be twice differentiable functions satisfying $f''(x) = g''(x)$ for all $x \in R$, $f'(1) = 2g'(1) = 4$ and $g(2) = 3f(2) = 9$. Then $f(25) - g(25)$ is equal to: