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Popular >

derivative of ln(xsqrt(x^2-7))

Solution

\frac{d}{d x} (ln (x x^{2} - 7))

Solution

\frac{2 x ^{2} - 7}{x ( x ^{2} - 7 )}

Solution steps

\frac{d}{d x} (ln (x x^{2} - 7))

Apply the chain rule:

\frac{1}{x x ^{2} - 7} \frac{d}{d x} (x x^{2} - 7)

= \frac{1}{x x ^{2} - 7} \frac{d}{d x} (x x^{2} - 7)

\frac{d}{d x} (x x^{2} - 7) = \frac{2 x ^{2} - 7}{x ^{2} - 7}

= \frac{1}{x x ^{2} - 7} \cdot \frac{2 x ^{2} - 7}{x ^{2} - 7}

Simplify

\frac{1}{x x ^{2} - 7} \cdot \frac{2 x ^{2} - 7}{x ^{2} - 7} : \frac{2 x ^{2} - 7}{x ( x ^{2} - 7 )}

= \frac{2 x ^{2} - 7}{x ( x ^{2} - 7 )}

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Frequently Asked Questions (FAQ)

What is the derivative of ln(xsqrt(x^2-7)) ?
The derivative of ln(xsqrt(x^2-7)) is (2x^2-7)/(x(x^2-7))
What is the first derivative of ln(xsqrt(x^2-7)) ?
The first derivative of ln(xsqrt(x^2-7)) is (2x^2-7)/(x(x^2-7))