What is (\partial)/(\partial x)(ln(x^3+y^5)) ?

The answer to (\partial)/(\partial x)(ln(x^3+y^5)) is (3x^2)/(x^3+y^5)

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(\partial)/(\partial x)(ln(x^3+y^5))

\frac{\partial}{\partial x} (ln (x^{3} + y^{5}))

\frac{3 x ^{2}}{x ^{3} + y ^{5}}

Solution steps

\frac{\partial}{\partial x} (ln (x^{3} + y^{5}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{3} + y ^{5}} \frac{\partial}{\partial x} (x^{3} + y^{5})

= \frac{1}{x ^{3} + y ^{5}} \frac{\partial}{\partial x} (x^{3} + y^{5})

\frac{\partial}{\partial x} (x^{3} + y^{5}) = 3 x^{2}

= \frac{1}{x ^{3} + y ^{5}} \cdot 3 x^{2}

Simplify

\frac{1}{x ^{3} + y ^{5}} \cdot 3 x^{2} : \frac{3 x ^{2}}{x ^{3} + y ^{5}}

= \frac{3 x ^{2}}{x ^{3} + y ^{5}}

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

\int_{0}^{1} 4 x 5^{x} d x

x \to - 2 lim (2 x + 4)

500 x - 0.003 x^{2} + 1 0^{- 8} x^{3}

\frac{d}{d x} (\frac{1}{3} \cdot (x - 5)^{3})

What is (\partial)/(\partial x)(ln(x^3+y^5)) ?
The answer to (\partial)/(\partial x)(ln(x^3+y^5)) is (3x^2)/(x^3+y^5)