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

The answer to (\partial)/(\partial y)(ln(x^4y)) is 1/y

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

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

\frac{1}{y}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{1}{y}

\frac{d}{d x} ((2 - 3 x^{2})^{4} (x^{7} + 3)^{3})

\frac{d y}{d x} + 7 y = 4

\frac{d}{d z} (z + 1 - 1)

x^{2} + 8 x + 2

x \to 1 - lim (\frac{∣ x - 1 ∣}{x - 1})

What is (\partial)/(\partial y)(ln(x^4y)) ?
The answer to (\partial)/(\partial y)(ln(x^4y)) is 1/y