Find (d y)/(d x) and (d^2 y)/(d x^2) given that [ x=a t^2 y=2 a t ]

Name: Find (d Y)/(d X) and (d^2 Y)/(d X^2) Given That [ X=a T^2 Y=2 a T ]
Brand: QuestionAI
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Question

Answer 1

To find

and

, we first need to find

and

.Given:

First, let's find

and

:

Now, we can find

by using the chain rule:

To find

, we take the reciprocal of

:

Now, substitute

and

into the equation for

:

Next, let's find

by differentiating

with respect to

:

Using the chain rule again, we have:

Now, substitute this into the equation for

:

So, the correct answers are:

Question