Mathematics, 06.01.2021 14:00 khyyonsb
Determine dz/dt for the two following mathematical relations: a) z = xe^xy, x = t^2, y = t^-1 b) z = x^2 y^3 + y cos x, x = ln (t^2), y = sin (4t)
Answers: 3
![\frac{dz}{dt} = [4\cdot \ln t\cdot \sin^{3} 4t - \sin 4t \cdot \sin (2\ln t)]\cdot \left(\frac{2}{t} \right)+[12\cdot (\ln t)^{2}\cdot \sin^{2} 4t + \cos (2\cdot \ln t)]\cdot (4\cdot \cos 4t)](/tpl/images/1015/9880/ed025.png)
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![\frac{dz}{dt} = \frac{dx}{dt}\cdot e^{x\cdot y} +x\cdot e^{x\cdot y}\cdot \left[\frac{dx}{dt}\cdot y+x\cdot \frac{dy}{dt} \right]](/tpl/images/1015/9880/2708a.png)
![\frac{dz}{dt} = e^{x\cdot y}\cdot \left\{\frac{dx}{dt}+x\cdot \left[\frac{dx}{dt}\cdot y+x\cdot \frac{dy}{dt} \right] \right\}](/tpl/images/1015/9880/0f2c1.png)
![\frac{dz}{dt} = e^{x\cdot y}\cdot \left[(1+x\cdot y)\cdot \frac{dx}{dt}+x\cdot \frac{dy}{dt} \right]](/tpl/images/1015/9880/687e5.png)
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![\frac{dz}{dt} = e^{t}\cdot \left[(1+t)\cdot 2\cdot t +t^{2}\cdot (-t^{-2})\right]](/tpl/images/1015/9880/fd8e7.png)
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Determine dz/dt for the two following mathematical relations: a) z = xe^xy, x = t^2, y = t^-1 b) z =...
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