Question

dx/dt = -2 , dy/dt = 3
If z^2=(x^2)(y^2), what is dz/dt when x=2, y=3

Answer 1

\[\Large z^2 = x^2*y^2\]
\[\Large \frac{d}{dt}[z^2] = \frac{d}{dt}[x^2*y^2]\]
\[\Large \frac{d}{dt}[z^2] = \frac{d}{dt}[x^2]*y^2+x^2*\frac{d}{dt}[y^2]\]
\[\Large 2z*\frac{dz}{dt} = 2x*\frac{dx}{dt}*y^2+x^2*2y*\frac{dy}{dt}\]
I'll let you finish up