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