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NDA 2010
Exam
NDA
Year
2010
Subject
Mathematics
Chapter
Differentiation

NDA 2010 · Mathematics · Differentiation

If x=t^2, y=t^3 , then what is (d^2 y)/(d x^2) equal to?

If x=t2,y=t3x=t^2, y=t^3, then what is d2ydx2\frac{d^2 y}{d x^2} equal to?

Options

  1. A1
  2. B32t\frac{3}{2 t}
  3. C34t\frac{3}{4 t}
  4. D32\frac{3}{2}

Correct answer

C. 34t\frac{3}{4 t}

Step-by-step solution

x=t2,y=t3∴dxdt=2t,dydt=3t2∴dydx=dy/dtdx/dt=3t22t=32×t\begin{aligned} & x=t^2, y=t^3 \\ & \therefore \frac{d x}{d t}=2 t, \frac{d y}{d t}=3 t^2 \\ & \therefore \frac{d y}{d x}=\frac{d y / d t}{d x / d t}=\frac{3 t^2}{2 t}=\frac{3}{2} \times t\end{aligned} Also, d2ydx2=32×1×dtdx=32×12t=34t\begin{aligned} & \text{ Also, } \frac{d^2 y}{d x^2}=\frac{3}{2} \times 1 \times \frac{d t}{d x} \\ & =\frac{3}{2} \times \frac{1}{2 t}=\frac{3}{4} t\end{aligned}$
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