What is (\partial)/(\partial x)(ln(x^6+y^3)) ?

The answer to (\partial)/(\partial x)(ln(x^6+y^3)) is (6x^5)/(x^6+y^3)

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(\partial)/(\partial x)(ln(x^6+y^3))

\frac{\partial}{\partial x} (ln (x^{6} + y^{3}))

\frac{6 x ^{5}}{x ^{6} + y ^{3}}

Solution steps

\frac{\partial}{\partial x} (ln (x^{6} + y^{3}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{x ^{6} + y ^{3}} \frac{\partial}{\partial x} (x^{6} + y^{3})

= \frac{1}{x ^{6} + y ^{3}} \frac{\partial}{\partial x} (x^{6} + y^{3})

\frac{\partial}{\partial x} (x^{6} + y^{3}) = 6 x^{5}

= \frac{1}{x ^{6} + y ^{3}} \cdot 6 x^{5}

Simplify

\frac{1}{x ^{6} + y ^{3}} \cdot 6 x^{5} : \frac{6 x ^{5}}{x ^{6} + y ^{3}}

= \frac{6 x ^{5}}{x ^{6} + y ^{3}}

sin (x) \frac{π}{4}

\int sec^{2} (11 x) d x

e^{- 9 t}

y = 3 + 6 x + 8 x e^{x}

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

What is (\partial)/(\partial x)(ln(x^6+y^3)) ?
The answer to (\partial)/(\partial x)(ln(x^6+y^3)) is (6x^5)/(x^6+y^3)