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Popular Calculus >

derivative of ln(xsqrt(x^2-5))

Solution

\frac{d}{d x} (ln (x x^{2} - 5))

Solution

\frac{2 x ^{2} - 5}{x ( x ^{2} - 5 )}

Solution steps

\frac{d}{d x} (ln (x x^{2} - 5))

Apply the chain rule:

\frac{1}{x x ^{2} - 5} \frac{d}{d x} (x x^{2} - 5)

= \frac{1}{x x ^{2} - 5} \frac{d}{d x} (x x^{2} - 5)

\frac{d}{d x} (x x^{2} - 5) = \frac{2 x ^{2} - 5}{x ^{2} - 5}

= \frac{1}{x x ^{2} - 5} \cdot \frac{2 x ^{2} - 5}{x ^{2} - 5}

Simplify

\frac{1}{x x ^{2} - 5} \cdot \frac{2 x ^{2} - 5}{x ^{2} - 5} : \frac{2 x ^{2} - 5}{x ( x ^{2} - 5 )}

= \frac{2 x ^{2} - 5}{x ( x ^{2} - 5 )}

Graph

Popular Examples

integral of 1/(xln^5(x))

\int \frac{1}{x ln ^{5} ( x )} d x

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d er i v a t i v e \frac{e ^{3 x^{2}}}{5 x}

slope of (19.3)(20.3)

s l o p e (19.3) (20.3)

derivative of sqrt(e^{sin(x)})

\frac{d}{d x} (e^{s i n (x)})

limit as x approaches 2 of (x-2)/((x-2))

x \to 2 lim (\frac{x - 2}{( x - 2 )})

Frequently Asked Questions (FAQ)

What is the derivative of ln(xsqrt(x^2-5)) ?
The derivative of ln(xsqrt(x^2-5)) is (2x^2-5)/(x(x^2-5))
What is the first derivative of ln(xsqrt(x^2-5)) ?
The first derivative of ln(xsqrt(x^2-5)) is (2x^2-5)/(x(x^2-5))