For some constants $a$ and $b$,find the derivative of $\frac{x-a}{x-b}$.

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:

If $f: R \rightarrow R$ is an even function having derivatives of all orders, then which of the following is an odd function?

Find the derivative: $\frac{d}{dx} \left( \frac{e^x}{1 + x^2} \right)$

If $y = \cos (\sin {x^2}),$ then at $x = \sqrt {\frac{\pi }{2}} , \frac{dy}{dx} = $

$\frac{d}{dx} \left( e^{\sqrt{1 - x^2}} \cdot \tan x \right)$