Question

If $x=a{t}^4,y=b{t}^3,then\frac{dy}{dx}=?$

• A. $\frac{3b}{4at}$
• B. $\frac{4at}{3b}$
• C. 12abt
• D. none of these

Answer 1

The correct option is A

$\frac{3b}{4at}$

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'

$\frac{dx}{dt}=4a{t}^3,\frac{dy}{dt}=3b{t}^2$
Diving $\frac{dy}{dt}by\frac{dx}{dt},\frac{dy}{dx}=\frac{dy}{dt}\times \frac{dt}{dx}=\frac{3b{t}^2}{4a{t}^3}=\frac{3b}{4at}$