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If y=at^2 and x=2at where x,y,t are variables and is a constant then find dy/dx ?

1 Answer

Jun 17, 2018

$\frac{d y}{d x} = t$ $dy/dx = t$

Explanation:

We have:

$y = a t^{2}$ $y= at^2$ and $x = 2 a t$ $x=2at$

Differentiating wrt $t$ $t$ we have:

$\frac{d y}{d t} = 2 a t$ $dy/dt= 2at$ and $\frac{d x}{d t} = 2 a$ $dx/dt=2a$

And, By the Chain rule, we have:

$\frac{d y}{d x} = \frac{d y / d t}{d x / d t}$ $dy/dx = (dy//dt)/(dx//dt)$

$\ \ \ \ \ \= (2at)/(2a)$

$\ \ \ \ \ \= t$

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