#### Question

If *x* = 2*at*, *y* = *at*^{2}, where *a* is a constant, then find \[\frac{d^2 y}{d x^2} \text { at }x = \frac{1}{2}\] ?

#### Solution

Here,

\[x = 2\text { at and y } = a t^2 \]

\[\text { Differentiating w . r . t . t, we get }\]

\[\frac{d x}{d t} = 2\text { a and} \frac{d y}{d t} = 2\text { at } \]

\[ \therefore \frac{d y}{d x} = \frac{2at}{2a} = t\]

\[\text { Differentiating again w . r . t . t, we get} \]

\[\frac{d^2 y}{d x^2} = 1 \times \frac{dt}{dx} = \frac{1}{2a}\]

\[\text { Now,} \left[ \frac{d^2 y}{d x^2} \right]_{x = \frac{1}{2}} = \frac{1}{2a}\]

Is there an error in this question or solution?

Solution for question: If X = 2at, Y = At2, Where a is a Constant, Then Find D 2 Y D X 2 at X = 1 2 ? concept: Simple Problems on Applications of Derivatives. For the courses CBSE (Commerce), CBSE (Arts), PUC Karnataka Science, CBSE (Science)