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

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

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

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

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

Solution steps

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

Treat

y, z

as constants

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

\frac{\partial}{\partial x} (z) = 0

= \frac{3 x ^{2}}{x ^{3} + y ^{3}} - 0

Simplify

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

\int x x^{2} - 9 d x

\frac{1}{( 1 + x ) ^{\frac{1}{2}}}

\frac{\partial}{\partial t} (\frac{t}{s})

\int \frac{1}{3 x ( 1 + 3 x )} d x

\int \frac{x + 2}{x - 2} (x^{2} - 4 x) d x

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