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Allushta [10]
3 years ago
11

Suppose w=xy+yzw=xy+yz, where x=e2t, y=2+sin(4t)x=e2t, y=2+sin⁡(4t), and z=2+cos(5t)z=2+cos⁡(5t).

Mathematics
1 answer:
Volgvan3 years ago
3 0
w(x,y,z)=xy+yz
x(t)=e^{2t}
y(t)=2+\sin4t
z(t)=2+\cos5t

\dfrac{\mathrm dw}{\mathrm dt}=\dfrac{\partial w}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial w}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}+\dfrac{\partial w}{\partial z}\dfrac{\mathrm dz}{\mathrm dt}

\dfrac{\mathrm dw}{\mathrm dt}=y\dfrac{\mathrm dx}{\mathrm dt}+(x+z)\dfrac{\mathrm dy}{\mathrm dt}+y\dfrac{\mathrm dz}{\mathrm dt}

\dfrac{\mathrm dw}{\mathrm dt}=2ye^{2t}+4(x+z)\cos4t-5y\sin5t
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