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  • Solve this problem - Limit , continuity and differentiability - JEE Main-15

Let x = at^{3}, y = bt^{2} then \frac{d^{2}y}{dx^{2}} =?

  • Option 1)

    -\frac{2b}{9a^{2}t^{4}}

  • Option 2)

    \frac{2b}{9a^{2}t^{4}}

  • Option 3)

    \frac{b}{9a^{2}t^{4}}

  • Option 4)

    none of these

 

Answers (1)

best_answer

As we have learnt,

 

Second order derivative for parametric function -

When we find 

\frac{dy}{dx}=F(t)\:then\:\frac{d^{2}y}{dx^{2}}=\frac{\frac{d}{dt}\:F(t)}{\frac{dx}{dt}}

-

 

 \frac{\mathrm{d} y}{\mathrm{d} x} =\frac{\frac{\mathrm{d}y }{\mathrm{d} t}}{\frac{\mathrm{d}x }{\mathrm{d} t}} = \frac{2bt}{3at^2} = \frac{2b}{3at}

\frac{\mathrm{d^2} y}{\mathrm{d} x^2} = \frac{\mathrm{d} }{\mathrm{d} x}\left (\frac{2b}{3at}\right ) = \frac{\frac{\mathrm{d} }{\mathrm{d} t}\left (\frac{2b}{3at}\right ) }{\frac{\mathrm{d} x}{\mathrm{d} t}} = \frac{\frac{-2b}{3at^2}}{3at^2} = \frac{-2b}{9a^2t^4}

 


Option 1)

-\frac{2b}{9a^{2}t^{4}}

Option 2)

\frac{2b}{9a^{2}t^{4}}

Option 3)

\frac{b}{9a^{2}t^{4}}

Option 4)

none of these

Posted by

Himanshu

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