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GUJCET · Maths · Continuity and Differentiability
\(\frac{d}{d x}\left(5^{\log x}\right)=\) ___________ .
- A \(\log 5 \cdot x^{\log (5 e)}\)
- B \(\log _x 5 \cdot 5^{\log x}\)
- C \(\log 5 \cdot x^{\log \left(\frac{5}{e}\right)}\)
- D \(\log 5 \cdot 5^{\log x}\)
Answer & Solution
Correct Answer
(C) \(\log 5 \cdot x^{\log \left(\frac{5}{e}\right)}\)
Step-by-step Solution
Detailed explanation
\(5^{\log x} = x^{\log 5}\) \(\frac{d}{dx}(x^{\log 5}) = \log 5 \cdot x^{\log 5 - 1}\)
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