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State whether the following is True or False: If y = log x, then dydx=1x - Mathematics and Statistics

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प्रश्न

State whether the following is True or False:

If y = log x, then `"dy"/"dx" = 1/"x"`

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
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उत्तर

True

shaalaa.com
The Concept of Derivative - Derivatives of Logarithmic Functions
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Differentiation - MISCELLANEOUS EXERCISE - 3 [पृष्ठ १००]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
अध्याय 3 Differentiation
MISCELLANEOUS EXERCISE - 3 | Q III] 6) | पृष्ठ १००

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∴ y = u + v

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`("d"y)/("d"x) = square/("d"x) + "dv"/square`   .....(i)

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log u = x × log x

Diff. w.r.to x,

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∴ `"du"/("d"x)` = u(1 + log x)

∴ `"du"/("d"x) = x^x (1 +  square)`    .....(ii)

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Diff.w.r.to x, we get

`"dv"/("d"x") = 20^square*log(20)`     .....(iii)

Substituting equations (ii) and (iii) in equation (i), we get

`("d"y)/("d"x)` = xx(1 + log x) + 20x.log(20)


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