hosiduy
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
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you mean
\[\frac{d^2z}{dt^2}\]
?
mukushla
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@hosiduy
hosiduy
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yes
mukushla
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just put x(t) and y(t) in the equation of z and take derivative twice
mukushla
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then what will u get?
hosiduy
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i still don't understand clear your way, can you make that more clear?
meera_yadav
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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
mukushla
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\[x=2 \ sint \\ y=3 \ \cos t \\ z(t)=3x^2+2y=3 (2 \ \sin t)^2+2( 3 \ \cos t)=12 \sin^2t+6 \cos t\]
mukushla
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@hosiduy
now take derivative of z(t) twice
am i clear now?
hosiduy
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oh, i understand now, thank all guys :D
mukushla
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yw