What is the derivative of ln(xsqrt(x^2-2)) ?

The derivative of ln(xsqrt(x^2-2)) is (2x^2-2)/(x(x^2-2))

What is the first derivative of ln(xsqrt(x^2-2)) ?

The first derivative of ln(xsqrt(x^2-2)) is (2x^2-2)/(x(x^2-2))

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\frac{d}{d x} (ln (x x^{2} - 2))

\frac{2 x ^{2} - 2}{x ( x ^{2} - 2 )}

Solution steps

\frac{d}{d x} (ln (x x^{2} - 2))

Apply the chain rule:

\frac{1}{x x ^{2} - 2} \frac{d}{d x} (x x^{2} - 2)

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

\frac{d}{d x} (x x^{2} - 2) = \frac{2 x ^{2} - 2}{x ^{2} - 2}

= \frac{1}{x x ^{2} - 2} \cdot \frac{2 x ^{2} - 2}{x ^{2} - 2}

Simplify

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

= \frac{2 x ^{2} - 2}{x ( x ^{2} - 2 )}

y^{^{''}} + 2 y^{^{'}} + 5 y = 2 sin (2 t)

\int tan^{2} (3 x) sec^{4} (3 x) d x

\int (csc^{2} (x) - 1) cot (x) d x

\frac{d}{d x} (\frac{1}{6 x - 7})

x \to - 1 lim (3 x^{2} - 3 x + 3)

What is the derivative of ln(xsqrt(x^2-2)) ?
The derivative of ln(xsqrt(x^2-2)) is (2x^2-2)/(x(x^2-2))
What is the first derivative of ln(xsqrt(x^2-2)) ?
The first derivative of ln(xsqrt(x^2-2)) is (2x^2-2)/(x(x^2-2))