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Popular >

derivative of y=ln(xsqrt(x^2-2))

Solution

derivative of

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

Solution

\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 )}

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(6, - 1), (8, 3)

derivative of (ln(x)/(x^{6/5)})

\frac{d}{d x} (\frac{ln ( x )}{x ^{\frac{6}{5}}})

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integral from 0 to 7 of sqrt(1+x)

\int_{0}^{7} 1 + x d x

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Frequently Asked Questions (FAQ)

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