What is (\partial)/(\partial x)(ln(x^4y)) ?

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

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(\partial)/(\partial x)(ln(x^4y))

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

\frac{4}{x}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{4} y} \frac{\partial}{\partial x} (x^{4} y)

= \frac{1}{x ^{4} y} \frac{\partial}{\partial x} (x^{4} y)

\frac{\partial}{\partial x} (x^{4} y) = 4 y x^{3}

= \frac{1}{x ^{4} y} \cdot 4 y x^{3}

Simplify

\frac{1}{x ^{4} y} \cdot 4 y x^{3} : \frac{4}{x}

= \frac{4}{x}

\frac{d}{d x} (x sinh (x) - 6 cosh (x))

\frac{d y}{d x} = 2 y^{2} + 3

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

\int \frac{x ^{2}}{2 + x} d x

\int \frac{x ^{2}}{x + 3} d x

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