यदि (If) `x=acos^(3)theta,y=asin^(3)theta`, (find) `(dy)/(dx)` ज्ञात करें ।

Explanation

`x=acos^(3)theta`
`therefore(dx)/(d theta)=a(d)/(d costheta)(cos^(3)theta)*(d)/(d theta)(costheta)`
या `(dx)/(d theta)=a.3cos^(2) theta(-sintheta)=-3a.cos^(2)theta.sintheta` … (1)
पुनः `y=asin^(3)theta`
`therefore(dy)/(d theta)=a(d (sin^(3)theta))/(dsintheta)*(d)/(d theta)(sintheta)`
या `(dy)/(d theta)=a.3sin^(2) theta.cos=3a sin^(2) thetacostheta` ... (2)
अब `(dy)/(dx)=((dy)/(d theta))/((dx)/(d theta))=(3a*sin^(2) theta*costheta)/(-3acos^(2) thetasin theta)=-tan theta`