What is (\partial)/(\partial x)(yln(x^3+y^3+8)-7) ?

The answer to (\partial)/(\partial x)(yln(x^3+y^3+8)-7) is (3yx^2)/(y^3+x^3+8)

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(\partial)/(\partial x)(yln(x^3+y^3+8)-7)

\frac{\partial}{\partial x} (y ln (x^{3} + y^{3} + 8) - 7)

\frac{3 y x ^{2}}{y ^{3} + x ^{3} + 8}

Solution steps

\frac{\partial}{\partial x} (y ln (x^{3} + y^{3} + 8) - 7)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (y ln (x^{3} + y^{3} + 8)) - \frac{\partial}{\partial x} (7)

\frac{\partial}{\partial x} (y ln (x^{3} + y^{3} + 8)) = \frac{3 y x ^{2}}{x ^{3} + y ^{3} + 8}

\frac{\partial}{\partial x} (7) = 0

= \frac{3 y x ^{2}}{x ^{3} + y ^{3} + 8} - 0

Simplify

= \frac{3 y x ^{2}}{y ^{3} + x ^{3} + 8}

\int y^{2} + 1 d y

\frac{d}{d x} ((5 + 3 x) cos (x))

\int_{0}^{1} \frac{x ^{3}}{x ^{2} + 2 x + 1} d x

f (x) = - \frac{12}{x ^{5}}

x \to 3 lim (∣ 3 - x ∣)

What is (\partial)/(\partial x)(yln(x^3+y^3+8)-7) ?
The answer to (\partial)/(\partial x)(yln(x^3+y^3+8)-7) is (3yx^2)/(y^3+x^3+8)