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AP EAMCET2011MathematicsApplication of Derivatives

The length of the subtangent at any point (x₁, y₁ ) on the curve y=5^x is

Options

  1. A5^ x₁
  2. By₁ 5^ x₁
  3. C_e 5
  4. D1 _e 5

Correct answer

D. 1 _e 5

Step-by-step solution

Given, y=5^x aligned & d y d x & =5^x 5 & ( d y d x )_ (x₁, y₁ ) & =5^ x₁ 5 aligned Length of subtangent =y₁ d x d y = y₁ 5^ x₁ 5 = 5^ x₁ 5^ x₁ 5 = 1 5

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