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

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mukushla
 3 years ago
Best ResponseYou've already chosen the best response.1you mean \[\frac{d^2z}{dt^2}\] ?

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.1just put x(t) and y(t) in the equation of z and take derivative twice

hosiduy
 3 years ago
Best ResponseYou've already chosen the best response.0i still don't understand clear your way, can you make that more clear?

meera_yadav
 3 years ago
Best ResponseYou've already chosen the best response.0hiii 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(sin2tsint) {2sint cost =sin2t} d^2z/dt^2 = 6(2cost2tcost) :) cheers

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.1\[x=2 \ sint \\ y=3 \ \cos t \\ z(t)=3x^2+2y=3 (2 \ \sin t)^2+2( 3 \ \cos t)=12 \sin^2t+6 \cos t\]

mukushla
 3 years ago
Best ResponseYou've already chosen the best response.1@hosiduy now take derivative of z(t) twice am i clear now?

hosiduy
 3 years ago
Best ResponseYou've already chosen the best response.0oh, i understand now, thank all guys :D
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