What is (\partial)/(\partial x)(ln(x^3+y)) ?

The answer to (\partial)/(\partial x)(ln(x^3+y)) is (3x^2)/(x^3+y)

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(\partial)/(\partial x)(ln(x^3+y))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{3} + y} \frac{\partial}{\partial x} (x^{3} + y)

= \frac{1}{x ^{3} + y} \frac{\partial}{\partial x} (x^{3} + y)

\frac{\partial}{\partial x} (x^{3} + y) = 3 x^{2}

= \frac{1}{x ^{3} + y} \cdot 3 x^{2}

Simplify

\frac{1}{x ^{3} + y} \cdot 3 x^{2} : \frac{3 x ^{2}}{x ^{3} + y}

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

- 3 x^{2}, at x = 2

\int (3 x + 5)^{2} d x

\frac{d}{d x} (x^{2} - 3 x - 5 x^{- 1} + 7 x^{- 2})

\frac{d y}{d x} = \frac{x ^{2} - 3}{6 y ^{2}}

\int_{0}^{1} \frac{x}{x + 1} d x

What is (\partial)/(\partial x)(ln(x^3+y)) ?
The answer to (\partial)/(\partial x)(ln(x^3+y)) is (3x^2)/(x^3+y)