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

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

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(\partial)/(\partial y)(x*ln(x+2y)+x/y)

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

\frac{2 x}{x + 2 y} - \frac{x}{y ^{2}}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{2 x}{x + 2 y} - \frac{x}{y ^{2}}

f (x) = \frac{1}{x + 2}

x \to 0 lim (2 x (1 - x))

\int_{1}^{\infty} x^{- \frac{1}{2}} d x

\int \frac{( u - 1 )}{( u + 1 )} d u

n = 1 \sum \infty 6 \frac{1}{n}

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