Method of Differentiation
Chain Rule
Premium Question
Grade 12
Question:
If $y = \tan^{-1}(\sqrt{x})$, then $\frac{dy}{dx}$ equals:
(1) $\frac{1}{1 + x}$
(2) $\frac{1}{2\sqrt{x}(1 + x)}$
(3) $\frac{1}{\sqrt{x}(1 + x)}$
(4) $\frac{1}{2(1 + x)}$
Step-by-Step Solution
Key Concept: Apply the chain rule by first differentiating $\tan^{-1}(u)$ with respect to $u = \sqrt{x}$, and then multiplying by $\frac{du}{dx}$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)