What is (\partial)/(\partial x)(x^2*y+(xe^x)/(y^3)) ?

The answer to (\partial)/(\partial x)(x^2*y+(xe^x)/(y^3)) is 2yx+(e^x+e^xx)/(y^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(\partial)/(\partial x)(x^2*y+(xe^x)/(y^3))

\frac{\partial}{\partial x} (x^{2} \cdot y + \frac{x e ^{x}}{y ^{3}})

2 y x + \frac{e ^{x} + e ^{x} x}{y ^{3}}

Solution steps

\frac{\partial}{\partial x} (x^{2} y + \frac{x e ^{x}}{y ^{3}})

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (x^{2} y) + \frac{\partial}{\partial x} (\frac{x e ^{x}}{y ^{3}})

\frac{\partial}{\partial x} (x^{2} y) = 2 y x

\frac{\partial}{\partial x} (\frac{x e ^{x}}{y ^{3}}) = \frac{e ^{x} + e ^{x} x}{y ^{3}}

= 2 y x + \frac{e ^{x} + e ^{x} x}{y ^{3}}

What is (\partial)/(\partial x)(x^2*y+(xe^x)/(y^3)) ?
The answer to (\partial)/(\partial x)(x^2*y+(xe^x)/(y^3)) is 2yx+(e^x+e^xx)/(y^3)