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

The answer to (\partial)/(\partial y)((ln(x+2y))/(y^2)) is (2(y-ln(x+2y)(x+2y)))/(y^3(x+2y))

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

\frac{\frac{2}{x + 2 y} y ^{2} - 2 y ln ( x + 2 y )}{( y ^{2} ) ^{2}} : \frac{2 ( y - ln ( x + 2 y ) ( x + 2 y ) )}{y ^{3} ( x + 2 y )}

= \frac{2 ( y - ln ( x + 2 y ) ( x + 2 y ) )}{y ^{3} ( x + 2 y )}

\int \frac{1}{e ^{x} - 3} d x

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

f (v) = e^{2 s i n (3 v)}

\int sin (x) - cos (x) d x

n = 1 \sum \infty (- 3)^{n}

What is (\partial)/(\partial y)((ln(x+2y))/(y^2)) ?
The answer to (\partial)/(\partial y)((ln(x+2y))/(y^2)) is (2(y-ln(x+2y)(x+2y)))/(y^3(x+2y))