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

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

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(\partial)/(\partial x)(ln(x^2+y^3))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{2} + y ^{3}} \frac{\partial}{\partial x} (x^{2} + y^{3})

= \frac{1}{x ^{2} + y ^{3}} \frac{\partial}{\partial x} (x^{2} + y^{3})

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

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

Simplify

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

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

\frac{\partial}{\partial x} (- 5 y cos (9 x))

x \to 3 lim (5 x^{2} - 9 x + 7)

f (x) = x + 6

\int \frac{1}{81 e ^{- 9 x} + e ^{9 x}} d x

\int_{- 2}^{3} \frac{29}{x ^{4}} d x

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