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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d t} = 4 y

n = 1 \sum \infty \frac{n + 1}{2 n + 1}

d er i v a t i v e y = x^{3 \cdot 7}

d er i v a t i v e f (x) = \frac{( x ^{2} - 3 x )}{2}

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

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