What is (\partial)/(\partial x)(xln(y)+y^2ln(x)) ?

The answer to (\partial)/(\partial x)(xln(y)+y^2ln(x)) is ln(y)+(y^2)/x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(xln(y)+y^2ln(x))

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

ln (y) + \frac{y ^{2}}{x}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x ln (y)) = ln (y)

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

= ln (y) + \frac{y ^{2}}{x}

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

\frac{d}{d x} ((3 x^{4} - 2) (1 + 4 x^{3}))

- \frac{14}{x ^{3}}

4 x^{5} + 11

\frac{\partial}{\partial x} (- 8 d (J + \frac{1}{2})^{2})

What is (\partial)/(\partial x)(xln(y)+y^2ln(x)) ?
The answer to (\partial)/(\partial x)(xln(y)+y^2ln(x)) is ln(y)+(y^2)/x