What is (\partial)/(\partial x)(2ln((x+y)^3)) ?

The answer to (\partial)/(\partial x)(2ln((x+y)^3)) is 6/(x+y)

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(\partial)/(\partial x)(2ln((x+y)^3))

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

\frac{6}{x + y}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{( x + y ) ^{3}} \frac{\partial}{\partial x} ((x + y)^{3})

= \frac{1}{( x + y ) ^{3}} \frac{\partial}{\partial x} ((x + y)^{3})

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

= 2 \cdot \frac{1}{( x + y ) ^{3}} \cdot 3 (x + y)^{2}

Simplify

2 \cdot \frac{1}{( x + y ) ^{3}} \cdot 3 (x + y)^{2} : \frac{6}{x + y}

= \frac{6}{x + y}

\frac{d}{d x} ((14 x - x^{2})^{3})

f (x) = 8 x^{2} + 8 x - 5, at x = - \frac{1}{2}

\frac{d}{d x} (\frac{4 x}{5 - tan ( x )})

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

\frac{d}{d x} (x + \frac{4}{x - 4})

What is (\partial)/(\partial x)(2ln((x+y)^3)) ?
The answer to (\partial)/(\partial x)(2ln((x+y)^3)) is 6/(x+y)