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BITSAT 2011
Exam
BITSAT
Year
2011
Subject
Mathematics
Chapter
Differentiation

BITSAT 2011 · Mathematics · Differentiation

If y=x^ x^2 , then ( (d y)/(d x) ) is equal to

If y=xx2y=x^{x^2}, then (dydx\frac{d y}{d x}) is equal to

Options

  1. A((2 \ln x))
  2. B((2 \ln x+1))
  3. C((\ln \ln x+1) x^{x^2})
  4. DNone of these

Correct answer

D. None of these

Step-by-step solution

Consider (y=x^{x^2} \Rightarrow \ln y=x² \ln x) 1ydydx=2xln⁡x+x2⋅1x=x(1+2ln⁡x)dydx=xx2⋅x(1+2ln⁡x)=xx2+1(1+2ln⁡x)\begin{aligned} \frac{1}{y} \frac{d y}{d x}=2 x \ln x+x² \cdot \frac{1}{x}=x(1+2 \ln x) \\ \frac{d y}{d x}=x^{x^2} \cdot x(1+2 \ln x)=x^{x^2+1}(1+2 \ln x) \end{aligned})
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