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

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

Popular >

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

f = x, g = ln (2 y - x)

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

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

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

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

Simplify

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

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

\frac{s - 3}{( s - 2 ) ^{2}}

x \to 0 lim (\frac{6 x - x ^{2}}{x})

t \to 1 lim (\frac{t ^{2} - 1}{1 - 1})

\frac{d}{d x} ((x + 2)^{a r c t a n (x)})

\frac{\partial}{\partial y} (\frac{2 x + 3}{4 y + 1})

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