Question

If z=x2+3xy+5y2 ,x=sin⁡(t),y=cos⁡(t) the total derivative dz/dt will become

Answer 1

Answer:

( 2x + 3y ) cos t  -  ( 3x + 10y ) sin t

Step-by-step explanation:

Given

            $z = x^2 + 3xy + 5y^2,\quad x=\sin t\ \text{and}\ y=\cos t.$

The total derivative dz/dt is

$\displaystyle\frac{dz}{dt}\ =\ \frac{\partial z}{\partial x}\frac{dx}{dt} + \frac{\partial z}{\partial y}\frac{dy}{dt}\ =\ (2x+3y)\cos t - (3x+10y)\sin t$

Hope this helps!