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

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

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(\partial)/(\partial x)(ln(x^3y+2z))

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

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

Solution steps

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

Treat

y, z

as constants

Apply the chain rule:

\frac{1}{x ^{3} y + 2 z} \frac{\partial}{\partial x} (x^{3} y + 2 z)

= \frac{1}{x ^{3} y + 2 z} \frac{\partial}{\partial x} (x^{3} y + 2 z)

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

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

Simplify

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

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

\int sin^{3} (3 x) cos (3 x) d x

x \to 0 lim (x^{2} tan (x))

\frac{8 x}{9 - tan ( x )}

x + 16, at x = 1

x \to 7 lim (ln (x - 7))

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