If `x=at^(4)`, `y=bt^(3)`, then find ` (dy)/(dx)`.

Explanation

This is called implicit differentiation or indirect differentiation. Here , both the given terms are differentiated independently w.r.t. a third variable and then combined together. Differentiating x and y w.r.t. t, we get
`(dx)/(dy)=4at^(3), " " (dy)/(dt)=3bt^(2)`
Dividing `(dy)/(dt)` by `(dx)/(dt)` , we get
`(dy)/(dx)=(dy)/(dt)xx(dt)/(dx)=(3bt^(2))/(4at^(3))=(3b)/(4at)`