What is (\partial)/(\partial x)(xln(x+6y)) ?

The answer to (\partial)/(\partial x)(xln(x+6y)) is ln(x+6y)+x/(x+6y)

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(\partial)/(\partial x)(xln(x+6y))

\frac{\partial}{\partial x} (x ln (x + 6 y))

ln (x + 6 y) + \frac{x}{x + 6 y}

Solution steps

\frac{\partial}{\partial x} (x ln (x + 6 y))

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = ln (x + 6 y)

= \frac{\partial}{\partial x} (x) ln (x + 6 y) + \frac{\partial}{\partial x} (ln (x + 6 y)) x

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (ln (x + 6 y)) = \frac{1}{x + 6 y}

= 1 \cdot ln (x + 6 y) + \frac{1}{x + 6 y} x

Simplify

1 \cdot ln (x + 6 y) + \frac{1}{x + 6 y} x : ln (x + 6 y) + \frac{x}{x + 6 y}

= ln (x + 6 y) + \frac{x}{x + 6 y}

y^{^{''}} - 5 y^{^{'}} = e^{5 x}

\frac{6}{( w ^{2} - 8 ) ^{4}}

f (x) = 7 e^{- x^{2}}

x^{2} + 2 x, x + 2, - 2, 1

\int_{49.75}^{x} 2 d x

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