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Question

If x=at4, y=bt3, then dydx=?


A

3b4at

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B

4at3b

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C

12abt

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D

none of these

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Solution

The correct option is A

3b4at


This is called implicit differentiation or indirect differentiation. Here both the terms given are differentiated independently w.r.t a third variable and then combined together. Differentiating x and y w.r.t 't'

dxdt=4at3, dydt=3bt2
Diving dydt by dxdt, dydx=dydt×dtdx=3bt24at3=3b4at


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