ashleyjahnaes5129 ashleyjahnaes5129
  • 12-08-2017
  • Mathematics
contestada

Use the chain rule to find dz/dt. z = 6 + x2 + y2 , x = 3 ln t, y = cos t

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LammettHash
LammettHash LammettHash
  • 13-08-2017
[tex]\dfrac{\mathrm dz}{\mathrm dt}=\dfrac{\partial z}{\partial x}\dfrac{\mathrm dx}{\mathrm dt}+\dfrac{\partial z}{\partial y}\dfrac{\mathrm dy}{\mathrm dt}[/tex]
[tex]=2x\left(\dfrac3t\right)+2y\left(-\sin t\right)[/tex]
[tex]=2(3\ln t)\left(\dfrac3t\right)+2\cos t(-\sin t)[/tex]
[tex]=\dfrac{18\ln t}t-2\cos t\sin t[/tex]
[tex]=\dfrac{18\ln t}t-\sin2t[/tex]
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