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

The answer to (\partial)/(\partial x)(xln(x/y)+xy^2) is ln(x/y)+1+y^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

ln (\frac{x}{y}) + 1 + y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x ln (\frac{x}{y})) = ln (\frac{x}{y}) + 1

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

= ln (\frac{x}{y}) + 1 + y^{2}

\frac{c e ^{- a s}}{s ^{2}}

n = 2 \sum \infty e^{5 - 6 n}

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

\int_{1}^{3} 9 arctan (1 x) d x

f (x) = x^{3} 1 - x^{2}

What is (\partial)/(\partial x)(xln(x/y)+xy^2) ?
The answer to (\partial)/(\partial x)(xln(x/y)+xy^2) is ln(x/y)+1+y^2