can anyone help me with this:
x = 2sin t;
y = 3cos t;
z(x,y) = 3x^2 + 2y
find: d(dz)/d^2(t)

Question

can anyone help me with this: 
x = 2sin t;
y = 3cos t;
z(x,y) = 3x^2 + 2y
find: d(dz)/d^2(t)

anonymous · Answer

you mean
$$\frac{d^2z}{dt^2}$$
?

anonymous · Answer

@hosiduy

anonymous · Answer

yes

anonymous · Answer

just put x(t) and y(t) in the equation of z and take derivative twice

anonymous · Answer

then what will u get?

anonymous · Answer

i still don't understand clear your way, can you make that more clear?

anonymous · Answer

hiii
z(x,y)=3 x^2+2y
first substitute the values of x and y in z(x,y), you'll get 
 z(t)=6sin^2t+6cost
dz/dt=6(2sint cost -sint)
=6(sin2t-sint)        {2sint cost =sin2t}
d^2z/dt^2 = 6(2cost2t-cost)
:) cheers

anonymous · Answer

$$x=2 \ sint \ y=3 \ \cos t \ z(t)=3x^2+2y=3 (2 \ \sin t)^2+2( 3 \ \cos t)=12 \sin^2t+6 \cos t$$

anonymous · Answer

@hosiduy 
now take derivative of z(t) twice
am i clear now?

anonymous · Answer

oh, i understand now, thank all guys :D

anonymous · Answer

yw