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MHT CET2010MathematicsDifferentiation

If x=f(t) and y=g(t) , then the value of d² y d x² is

Options

  1. Af^ (t) g^ (t) g^ (t) f^ (t) f^ (t) ³
  2. Bf^ (t) g^ (t)-g^ (t) f^ (t) f^ (t) ²
  3. Cg^ (t) f^ (t) g^ (t) f^ (t) f^ (t) ²
  4. Dg^ (t) f^ (t)-g^ (t) f^ (t) f^ (t) ³

Correct answer

A. f^ (t) g^ (t) g^ (t) f^ (t) f^ (t) ³

Step-by-step solution

Given, x=f(t), y=g(t) array c d x d t =f^ (t), d y d t =g^ (t) d y d x = g^ (t) f^ (t) array Now, d² y d x² = d d x ( d y d x ) aligned &= d d t ( g^ (t) f^ (t) ) d t d x =& [ f^ (t) g^ (t)-g^ (t) f^ (t) [f^ (t) ]² ] 1 f^ (t) =& f^ (t) g^ (t)-g^ (t) f^ (t) f^ (t) ³ aligned

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