What is (\partial)/(\partial x)(4ln(xy)) ?

The answer to (\partial)/(\partial x)(4ln(xy)) is 4/x

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(\partial)/(\partial x)(4ln(xy))

\frac{\partial}{\partial x} (4 ln (x y))

\frac{4}{x}

Solution steps

\frac{\partial}{\partial x} (4 ln (x y))

Treat

y

as a constant

Take the constant out:

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

= 4 \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

= 4 \cdot \frac{1}{x y} y

Simplify

4 \cdot \frac{1}{x y} y : \frac{4}{x}

= \frac{4}{x}

x^{3} - 6 x^{2} - 34 x + 40, at x = 6

\int - k x d x

\int \frac{1}{x ( x + 1 )} d x

x \to 0 lim (\frac{( x + 5 )}{3 x})

y = (t^{2} + 3) e^{t}

What is (\partial)/(\partial x)(4ln(xy)) ?
The answer to (\partial)/(\partial x)(4ln(xy)) is 4/x