What is (\partial)/(\partial x)(2xyln(x)) ?

The answer to (\partial)/(\partial x)(2xyln(x)) is 2y(ln(x)+1)

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(\partial)/(\partial x)(2xyln(x))

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

2 y (ln (x) + 1)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = ln (x)

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

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

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

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

Simplify

2 y (1 \cdot ln (x) + \frac{1}{x} x) : 2 y (ln (x) + 1)

= 2 y (ln (x) + 1)

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\frac{d}{d x} (\frac{8 x}{7 - tan ( x )})

What is (\partial)/(\partial x)(2xyln(x)) ?
The answer to (\partial)/(\partial x)(2xyln(x)) is 2y(ln(x)+1)