If \(y = (x^{2} + 1)^{3/2}\), then \(\displaystyle\frac{dy}{dx}\) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(3x\sqrt{x^{2} + 1}\)
By the chain rule, with \(u = x^{2} + 1\):
\( \displaystyle \frac{dy}{dx} = \frac{3}{2}(x^{2} + 1)^{1/2} \cdot 2x \)
\( \displaystyle = 3x\sqrt{x^{2} + 1} \)