Find `(dy)/(dx)` , when `x=a t^2` and `y=2\ a t`

Explanation

We can write `dy/dx`as

`frac{d y}{d x}=frac{d y}{d x} times frac{d t}{d t} `

`frac{d y}{d x}=frac{d y}{d t} times frac{d t}{d x}`


`frac{d y}{d x}=frac{frac{d y}{d t}}{frac{d x}{d t}}`

Now calculate `dy/dt`

`y =2 a t `
` frac{d y}{d t} =frac{d(2 a t)}{d t} `
` frac{d y}{d t} =2 a cdot frac{d(t)}{d t} `
`frac{d y}{d t} =mathbf{2 a} `

Calculating`dx/dt`

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