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

The answer to (\partial)/(\partial x)(ln(2x^3+y)) is (6x^2)/(2x^3+y)

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

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

\frac{6 x ^{2}}{2 x ^{3} + y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (2 x^{3} + y) = 6 x^{2}

= \frac{1}{2 x ^{3} + y} \cdot 6 x^{2}

Simplify

\frac{1}{2 x ^{3} + y} \cdot 6 x^{2} : \frac{6 x ^{2}}{2 x ^{3} + y}

= \frac{6 x ^{2}}{2 x ^{3} + y}

f (x) = (- 25 x^{2} + 9)^{2}

\frac{\partial}{\partial x} (1 - x - y)

\frac{4}{s + 2}

\int \frac{2000}{1 + 0.3 e ^{- 0.276 t}} d t

\frac{\partial}{\partial x} ((x yz)^{\frac{1}{2}})

What is (\partial)/(\partial x)(ln(2x^3+y)) ?
The answer to (\partial)/(\partial x)(ln(2x^3+y)) is (6x^2)/(2x^3+y)