Question

if x=asex^3teta, y=atan^3teta, find dy/dx​

Answer 1

Step-by-step explanation:

Let, y = tan^3 theta

x = sec^3 theta

Now,

Diff y wrt theta, we get

dy/d (theta) = 3 tan^2 theta × sec^2 theta

Diff x wrt theta, we get

dx/d (theta) = 3 sec^2 theta × sec theta × tan theta = 3 sec^3 theta × tan theta

Now derivative of tan^3 theta wrt sec^3 theta is,

dy/dx = (dy/d theta) / (dx/d theta)

dy/dx = 3 tan^2 theta × sec^2 theta / 3 sec^3 theta × tan theta

dy/dx = tan theta / sec theta

At theta = π/3

dy/dx = √3 / 2 (ans)

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