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

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

Popular >

(\partial)/(\partial x)((u)(ln(x)+ln(y)))

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

\frac{u}{x}

Solution steps

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

Simplify

(u) (ln (x) + ln (y)) : u ln (x y)

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

Treat

u, y

as constants

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= u \frac{1}{x y} y

Simplify

u \frac{1}{x y} y : \frac{u}{x}

= \frac{u}{x}

\frac{1}{3} ln (\frac{7}{6} + \frac{5}{2})

3 x^{2} y sin (5 x) - ln (4 y)

3 ln ∣ x - 2 ∣ + 4 ln ∣ x + 7 ∣

4.3 + lo g_{10} (\frac{0.02}{0.05})

\frac{1}{2} ln (x) + 8 ln (x^{3}) - 3 ln (x - 2)

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