Find the derivative of $f(x) = 3$ at $x = 0$ and at $x = 3$.

Let $g(x) \neq 0, g^{\prime}(x) \neq 0, f(x) \neq 0, f^{\prime}(x) \neq 0$. If $F(x)=f(x) g(x)$, $G(x)=f^{\prime}(x) g^{\prime}(x)$, $F^{\prime}(x)=G(x) H(x)$, and $F^{\prime}(x)=F(x) K(x)$, then $H(x)+K(x)=$

$\frac{d}{dx} \log_{\sqrt{x}} \left(\frac{1}{x}\right)$ is equal to

Differentiating the following with respect to $x$: $\frac{\cos x}{\log x}, x > 0$

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

If $f(x) = e^x g(x)$,$g(0) = 2$,and $g'(0) = 1$,then $f'(0)$ is