Question

if x=at^3, y=3bt^2 then dy/dx
a) 3x/2y
b) 2y/3x
c) 3y/2x
d) 2x/3y

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Answer 1

Answer:

$x = at {}^{3}$

$y = 3bt {}^{2}$

$\frac{dy}{dx} =?$

Differnatatiating with respect to " t "

$\frac{dx}{dt} = \frac{d(at {}^{3}) }{dt}$

$\frac{dx}{dt} = 3 \times at {}^{2}$

$\frac{dx}{dt} = 3at {}^{2}$

Now,

$\frac{dy}{dt} = \frac{d(3bt {}^{2} )}{dt}$

$\frac{dy}{dt} = 2 \times 3bt$

$\frac{dy}{dt} = 6bt$

Now,

$\frac{dy}{dx} = \frac{6bt}{3at {}^{2} }$

$\frac{dy}{dx} = \frac{2b}{at}$

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