TS EAMCET · Maths · Application of Derivatives
The length of the subtangent at any point \(\left(x_1, y_1\right)\) on the curve \(y=5^x\) is
- A \(5^{x_1}\)
- B \(y_1 5^{x_1}\)
- C \(\log _e 5\)
- D \(\frac{1}{\log _e 5}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{\log _e 5}\)
Step-by-step Solution
Detailed explanation
Given, \(y=5^x\) \(\begin{aligned} \Rightarrow & \frac{d y}{d x} & =5^x \log 5 \\ \Rightarrow & \left(\frac{d y}{d x}\right)_{\left(x_1, y_1\right)} & =5^{x_1} \log 5 \end{aligned}\) \(\therefore\) Length of subtangent…
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