Let $\theta = \tan^{-1}x$, so $\tan\theta = x$ and $y = \sec\theta$.

$\frac{dy}{dx} = \sec\theta\tan\theta\cdot\frac{d\theta}{dx} = \sec\theta\tan\theta\cdot\frac{1}{1+x^2}$

Since $\tan\theta=x$ and $\sec\theta=\sqrt{1+x^2}$:

$\frac{dy}{dx} = \sqrt{1+x^2}\cdot x\cdot\frac{1}{1+x^2} = \frac{x}{\sqrt{1+x^2}}$

At $x=1$: $\frac{dy}{dx} = \frac{1}{\sqrt{2}}$

The Heuristic method (from the Greek heuriskein, to discover) is based on the principle of learning by doing. Students discover knowledge through their own investigation and experimentation rather than being told the answers. It promotes active, experiential, and self-directed learning.

Correct Answer: A — Learning by doing.

The Holliday-Segar method calculates maintenance fluid requirements:

Calculation for 12 kg child:

\[\text{First 10 kg} = 10 \times 100 = 1000\,\text{mL}\]

\[\text{Next 2 kg} = 2 \times 50 = 100\,\text{mL}\]

\[\text{Total} = 1000 + 100 = 1100\,\text{mL/day}\]

Hourly rate: \(\dfrac{1100}{24} \approx 46\,\text{mL/hr}\)

This formula is essential for pediatric nurses. Remember: it calculates maintenance only — deficit and ongoing losses are added separately in dehydrated children.