What is the derivative of y=ln(xsqrt(x^2-4)) ?

The derivative of y=ln(xsqrt(x^2-4)) is (2x^2-4)/(x(x^2-4))

What is the first derivative of y=ln(xsqrt(x^2-4)) ?

The first derivative of y=ln(xsqrt(x^2-4)) is (2x^2-4)/(x(x^2-4))

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derivative of

y = ln (x x^{2} - 4)

\frac{2 x ^{2} - 4}{x ( x ^{2} - 4 )}

Solution steps

\frac{d}{d x} (ln (x x^{2} - 4))

Apply the chain rule:

\frac{1}{x x ^{2} - 4} \frac{d}{d x} (x x^{2} - 4)

= \frac{1}{x x ^{2} - 4} \frac{d}{d x} (x x^{2} - 4)

\frac{d}{d x} (x x^{2} - 4) = \frac{2 x ^{2} - 4}{x ^{2} - 4}

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

Simplify

\frac{1}{x x ^{2} - 4} \cdot \frac{2 x ^{2} - 4}{x ^{2} - 4} : \frac{2 x ^{2} - 4}{x ( x ^{2} - 4 )}

= \frac{2 x ^{2} - 4}{x ( x ^{2} - 4 )}

What is the derivative of y=ln(xsqrt(x^2-4)) ?
The derivative of y=ln(xsqrt(x^2-4)) is (2x^2-4)/(x(x^2-4))
What is the first derivative of y=ln(xsqrt(x^2-4)) ?
The first derivative of y=ln(xsqrt(x^2-4)) is (2x^2-4)/(x(x^2-4))