# If U = R 2 Cos 2 θ , V = R 2 Sin 2 θ . Find ∂ ( U , V ) ∂ ( R , θ ) - Applied Mathematics 1

Sum

If u=r^2cos2theta, v=r^2sin2theta. "find"(del(u,v))/(del(r,theta))

#### Solution

u=r^2cos2theta     v=r^2sin2theta

Diff. u and v w.r.t r and 𝜽 partially to apply it in jacobian

(del(u,v))/(del(r,theta))=|(u_r,u_theta),(v_r,v_theta)|=|(2rcos2theta,-2r^2sin2theta),(2rsin2theta,2r^2cos2theta)|

=4r^3cos^2 2theta+4r^3sin^2 2theta

=4r^3(cos^2 2theta+sin^2 2theta)

(del(u,v))/(del(r,theta))=4r^3

Concept: Jacobian
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