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

Simplificar

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

Encontre a primeira derivada parcial tratando a vari \overset{a}{ˊ} vel y como uma constante e diferenciando em rela \overset{c}{¸} \overset{a}{˜} o a x

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

Use a regra de diferencia \overset{c}{¸} \overset{a}{˜} o \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))

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

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

Calcule

More Steps

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

Calcule

More Steps

\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}