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

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

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(\partial)/(\partial x)(ln(e^x+xy^3))

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d s} (ln (1 + \frac{1}{s ^{2}}))

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

\int cos (\frac{π x}{2}) d x

\frac{d y}{d x} = 16 x sec^{2} (4 x)

\frac{d}{d x} (y sinh (x^{2}))

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