Solve w=e^x+x\ln{y}+y\ln{x}

Menyederhanakan

w = e^{x} + x ln (y) + y ln (x)

Carilah turunan parsial pertama dengan memperlakukan variabel y sebagai konstanta dan melakukan diferensiasi terhadap x .

\frac{\partial w}{\partial x} = \frac{\partial}{\partial x} (e^{x} + x ln (y) + y ln (x))

Gunakan aturan diferensiasi \frac{\partial}{\partial x} (f (x) \pm g (x)) = \frac{\partial}{\partial x} (f (x)) \pm \frac{\partial}{\partial x} (g (x))

\frac{\partial w}{\partial x} = \frac{\partial}{\partial x} (e^{x}) + \frac{\partial}{\partial x} (x ln (y)) + \frac{\partial}{\partial x} (y ln (x))

Gunakan \frac{\partial}{\partial x} e^{x} = e^{x} untuk mencari turunan

\frac{\partial w}{\partial x} = e^{x} + \frac{\partial}{\partial x} (x ln (y)) + \frac{\partial}{\partial x} (y ln (x))

Evaluasi

Mais Passos

\frac{\partial w}{\partial x} = e^{x} + ln (y) + \frac{\partial}{\partial x} (y ln (x))

Evaluasi

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\frac{\partial w}{\partial x} = e^{x} + ln (y) + \frac{y}{x}

Solução

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\frac{\partial w}{\partial x} = \frac{e ^{x} x + ln ( y ) \times x + y}{x}

W=e^x+x\ln{y}+y\ln{x}