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

Simplificar

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

Encuentre la primera derivada parcial tratando la variable y como una constante y diferenciando con respecto a x

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

Usar la regla de diferenciaci \overset{o}{ˊ} n \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))

Usa \frac{\partial}{\partial x} e^{x} = e^{x} para encontrar la derivada

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

Evalúe

More Steps

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

Evalúe

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

Solution

More Steps

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

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