What is the derivative of ln(xsqrt(x^2-10)) ?

The derivative of ln(xsqrt(x^2-10)) is (2x^2-10)/(x(x^2-10))

What is the first derivative of ln(xsqrt(x^2-10)) ?

The first derivative of ln(xsqrt(x^2-10)) is (2x^2-10)/(x(x^2-10))

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\frac{d}{d x} (ln (x x^{2} - 10))

\frac{2 x ^{2} - 10}{x ( x ^{2} - 10 )}

Solution steps

\frac{d}{d x} (ln (x x^{2} - 10))

Apply the chain rule:

\frac{1}{x x ^{2} - 10} \frac{d}{d x} (x x^{2} - 10)

= \frac{1}{x x ^{2} - 10} \frac{d}{d x} (x x^{2} - 10)

\frac{d}{d x} (x x^{2} - 10) = \frac{2 x ^{2} - 10}{x ^{2} - 10}

= \frac{1}{x x ^{2} - 10} \cdot \frac{2 x ^{2} - 10}{x ^{2} - 10}

Simplify

\frac{1}{x x ^{2} - 10} \cdot \frac{2 x ^{2} - 10}{x ^{2} - 10} : \frac{2 x ^{2} - 10}{x ( x ^{2} - 10 )}

= \frac{2 x ^{2} - 10}{x ( x ^{2} - 10 )}

f (x) = 4 x^{2} - 3 x + 2

\int_{0}^{5} x^{2} d x

\frac{d}{d x} (y^{1 - n})

\int - \frac{x ^{3}}{3 e ^{\frac{x}{2}}} d x

\frac{d}{d q} (500 q - \frac{q ^{2}}{ln ( q + 300 )})

What is the derivative of ln(xsqrt(x^2-10)) ?
The derivative of ln(xsqrt(x^2-10)) is (2x^2-10)/(x(x^2-10))
What is the first derivative of ln(xsqrt(x^2-10)) ?
The first derivative of ln(xsqrt(x^2-10)) is (2x^2-10)/(x(x^2-10))