Question

Determine $\dfrac{\Delta z}{\Delta t}$ de z=sen(3x+2y), x=tg(t) e y=cos(t)

Answer 1

z=sen(3x+2y)    

x=tg(t) e y =cos(t)

x= sen(t)/cos(t)

dx/dt=[cos(t)*cos(t) -sen(t) *(-sen(t))]/cos²(t)

dx/dt=[cos²(t) +sen²(t)]/cos²(t)

dx/dt=1/cos²(t)= sec²(t)

y =cos(t)

dy/dt= -sen(t)

dz/dt=(3x+2y)' * cos(3x+2y)

dz/dt=(3 * dx/dt+2*dy/dt) * cos(3x+2y)

dz/dt=(3 * sec²(t)-2*sen(t)) * cos(3x+2y)

dz/dt=(3 * sec²(t)-2*sen(t)) * cos[3*tg(t)+2*cos(t)]