Grade 12Differential Calculus
If x=(3at)/(a+t^3) and y=(3at^2)/(a+t^3) find dy/dx
1 Answer
bharat bajaj
First find dy/dt,
dy/dt = (a+t^3). 6at - 3at^2 ( 3t^2) / (a+t^3)^2
dx/dt = (a+t^3)(3a) - 3at(3t^2)/(a+t^3)^2
Now divide both:
dy/dx = (6a^2t -3at^4)/ (3a^2 -3at^3)
dy/dt = (a+t^3). 6at - 3at^2 ( 3t^2) / (a+t^3)^2
dx/dt = (a+t^3)(3a) - 3at(3t^2)/(a+t^3)^2
Now divide both:
dy/dx = (6a^2t -3at^4)/ (3a^2 -3at^3)
Thanks
Bharat Bajaj
IIT Delhi
askiitians faculty
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