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Popular >

derivative of ln(xsqrt(x^2-12))

Solution

\frac{d}{d x} (ln (x x^{2} - 12))

Solution

\frac{2 x ^{2} - 12}{x ( x ^{2} - 12 )}

Solution steps

\frac{d}{d x} (ln (x x^{2} - 12))

Apply the chain rule:

\frac{1}{x x ^{2} - 12} \frac{d}{d x} (x x^{2} - 12)

= \frac{1}{x x ^{2} - 12} \frac{d}{d x} (x x^{2} - 12)

\frac{d}{d x} (x x^{2} - 12) = \frac{2 x ^{2} - 12}{x ^{2} - 12}

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

Simplify

\frac{1}{x x ^{2} - 12} \cdot \frac{2 x ^{2} - 12}{x ^{2} - 12} : \frac{2 x ^{2} - 12}{x ( x ^{2} - 12 )}

= \frac{2 x ^{2} - 12}{x ( x ^{2} - 12 )}

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Frequently Asked Questions (FAQ)

What is the derivative of ln(xsqrt(x^2-12)) ?
The derivative of ln(xsqrt(x^2-12)) is (2x^2-12)/(x(x^2-12))
What is the first derivative of ln(xsqrt(x^2-12)) ?
The first derivative of ln(xsqrt(x^2-12)) is (2x^2-12)/(x(x^2-12))