What is (\partial)/(\partial x)(ln(6x^2-4y^2)) ?

The answer to (\partial)/(\partial x)(ln(6x^2-4y^2)) is (6x)/(3x^2-2y^2)

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(\partial)/(\partial x)(ln(6x^2-4y^2))

\frac{\partial}{\partial x} (ln (6 x^{2} - 4 y^{2}))

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

Solution steps

\frac{\partial}{\partial x} (ln (6 x^{2} - 4 y^{2}))

Treat

y

as a constant

Apply the chain rule:

\frac{1}{6 x ^{2} - 4 y ^{2}} \frac{\partial}{\partial x} (6 x^{2} - 4 y^{2})

= \frac{1}{6 x ^{2} - 4 y ^{2}} \frac{\partial}{\partial x} (6 x^{2} - 4 y^{2})

\frac{\partial}{\partial x} (6 x^{2} - 4 y^{2}) = 12 x

= \frac{1}{6 x ^{2} - 4 y ^{2}} \cdot 12 x

Simplify

\frac{1}{6 x ^{2} - 4 y ^{2}} \cdot 12 x : \frac{6 x}{3 x ^{2} - 2 y ^{2}}

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

x \to 7 lim (\frac{9 x}{x - 7})

\frac{d y}{d x} = e^{- x} - y

y = x^{\frac{17}{18}}

\frac{\partial}{\partial y} (y \cdot ln (x))

\frac{d}{d x} (\frac{1}{3} (16 + x^{2})^{3})

What is (\partial)/(\partial x)(ln(6x^2-4y^2)) ?
The answer to (\partial)/(\partial x)(ln(6x^2-4y^2)) is (6x)/(3x^2-2y^2)