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Question 93Asked in BPSC TRE 3.0 (2024) Mathematics Class 11-12

Differentiation of xˣ with respect to x, isxˣ का x के सापेक्ष अवकलन है

xˣ का x के सापेक्ष अवकलन है
  1. Axˣ(1 + logₑ x)xˣ(1 + logₑ x)
  2. Bxˣ(1 − logₑ x)xˣ(1 − logₑ x)
  3. Cx⁻ˣx⁻ˣ
  4. DMore than one of the aboveउपर्युक्त में से एक से अधिक
  5. ENone of the aboveउपर्युक्त में से कोई नहीं
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Correct answer: (A) xˣ(1 + logₑ x)xˣ(1 + logₑ x)

Explanation

Let y = xˣ, so log y = x log x. Differentiating, (1/y) dy/dx = log x + 1, hence dy/dx = xˣ(1 + logₑ x).मान लें y = xˣ, तो log y = x log x। अवकलन करने पर (1/y) dy/dx = log x + 1, इसलिए dy/dx = xˣ(1 + logₑ x)।

From BPSC TRE 3.0 (2024) Mathematics Class 11-12 — Previous Year Paper

This is question 93 of BPSC TRE 3.0 (2024) Mathematics Class 11-12 — Previous Year Paper. See all questions of this paper with answers, or attempt the paper as a timed online test to get your score and all-India rank.