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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

\frac{1}{x + 2 y} \frac{\partial}{\partial y} (x + 2 y)

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

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

= x \frac{1}{x + 2 y} \cdot 2

Simplify

x \frac{1}{x + 2 y} \cdot 2 : \frac{2 x}{x + 2 y}

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

\frac{d}{d t} ((t + sin (t - 1))^{3} (t^{2} - 2)^{5})

\int x \cdot ln (x^{2} + 1) d x

\int_{0}^{1} ln (2 x + 1) d x

f (x) = - 4 x^{2} - 3 + 2, at x = - 1

\int_{0}^{1} \frac{x + 1}{x ^{2} + 1} d x

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