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Popular >

derivative of ln(xsqrt(x^2-8))

Solution

\frac{d}{d x} (ln (x x^{2} - 8))

Solution

\frac{2 x ^{2} - 8}{x ( x ^{2} - 8 )}

Solution steps

\frac{d}{d x} (ln (x x^{2} - 8))

Apply the chain rule:

\frac{1}{x x ^{2} - 8} \frac{d}{d x} (x x^{2} - 8)

= \frac{1}{x x ^{2} - 8} \frac{d}{d x} (x x^{2} - 8)

\frac{d}{d x} (x x^{2} - 8) = \frac{2 x ^{2} - 8}{x ^{2} - 8}

= \frac{1}{x x ^{2} - 8} \cdot \frac{2 x ^{2} - 8}{x ^{2} - 8}

Simplify

\frac{1}{x x ^{2} - 8} \cdot \frac{2 x ^{2} - 8}{x ^{2} - 8} : \frac{2 x ^{2} - 8}{x ( x ^{2} - 8 )}

= \frac{2 x ^{2} - 8}{x ( x ^{2} - 8 )}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of ln(xsqrt(x^2-8)) ?
The derivative of ln(xsqrt(x^2-8)) is (2x^2-8)/(x(x^2-8))
What is the first derivative of ln(xsqrt(x^2-8)) ?
The first derivative of ln(xsqrt(x^2-8)) is (2x^2-8)/(x(x^2-8))