Question:medium
If \(s = \sqrt{t + 1}, x = \log s\) and \(y = 6x + 3\), then \(\frac{dy}{dt} =\)
If \(s = \sqrt{t + 1}, x = \log s\) and \(y = 6x + 3\), then \(\frac{dy}{dt} =\)
Show Hint
Always simplify logarithmic expressions before differentiating. Using \(\log(\sqrt{u}) = \frac{1}{2}\log u\) turns a messy chain rule problem into a simple single-step derivative.
Updated On: Jun 24, 2026
- \(\frac{2}{\sqrt{t + 1}}\)
- \(\frac{6}{t + 1}\)
- \(3\sqrt{t + 1}\)
- \(\frac{3}{t + 1}\)
- \(\frac{3}{\sqrt{t + 1}}\)
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The Correct Option is D
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