What is (\partial)/(\partial x)(z^3ln(xy)) ?

The answer to (\partial)/(\partial x)(z^3ln(xy)) is (z^3)/x

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(\partial)/(\partial x)(z^3ln(xy))

\frac{\partial}{\partial x} (z^{3} ln (x y))

\frac{z ^{3}}{x}

Solution steps

\frac{\partial}{\partial x} (z^{3} ln (x y))

Treat

z, y

as constants

Take the constant out:

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

= z^{3} \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

= z^{3} \frac{1}{x y} y

Simplify

z^{3} \frac{1}{x y} y : \frac{z ^{3}}{x}

= \frac{z ^{3}}{x}

f (x) = - 2 x^{2} - 5 x + 2

\int_{0}^{2} 4^{- θ} d θ

\int (3 x^{2} - 1) d x

f (x) = 2 x^{3} + 4 x^{2} + 6 x

x \to 0 + lim (sin (\frac{5 π}{6} e^{x}))

What is (\partial)/(\partial x)(z^3ln(xy)) ?
The answer to (\partial)/(\partial x)(z^3ln(xy)) is (z^3)/x