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

Đơn giản hóa

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

T \overset{ı}{ˋ} m đ ạo h \overset{a}{ˋ} m ri \overset{e}{ˆ} ng đ \overset{ˋ}{\overset{a}{ˆ}} u ti \overset{e}{ˆ} n b \overset{ˋ}{\overset{a}{˘}} ng c \overset{a}{ˊ} ch coi bi \overset{ˊ}{\overset{e}{ˆ}} n y l \overset{a}{ˋ} h \overset{ˋ}{\overset{a}{˘}} ng s \overset{ˊ}{\overset{o}{ˆ}} v \overset{a}{ˋ} l \overset{ˊ}{\overset{a}{ˆ}} y đ ạo h \overset{a}{ˋ} m đ \overset{ˊ}{\overset{o}{ˆ}} i với x

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

Sử dụng quy t \overset{ˊ}{\overset{a}{˘}} c ph \overset{a}{ˆ} n biệt \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))

Sử dụng \frac{\partial}{\partial x} e^{x} = e^{x} đ ể t \overset{ı}{ˋ} m đ ạo h \overset{a}{ˋ} m

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

Tính

Mais Passos

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

Tính

Mais Passos

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

Solução

Mais Passos

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

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