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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{3 y ^{2} - x ^{3} - 3} (- 3 x^{2}) : - \frac{3 x ^{2}}{3 y ^{2} - x ^{3} - 3}

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

x \to 0 lim (\frac{5 ^{x} - 1 3 ^{x}}{x})

x \to 0 lim (x \cdot sin (\frac{1}{x}))

\frac{\partial}{\partial x} (ln (x) - 4)

\frac{d}{d x} (y^{5} sin (5 x))

\frac{\partial}{\partial x} (4 sin (4 x) e^{3 x})

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