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Popular >

derivative of ln(xsqrt(x^2-9))

Solution

\frac{d}{d x} (ln (x x^{2} - 9))

Solution

\frac{2 x ^{2} - 9}{x ( x ^{2} - 9 )}

Solution steps

\frac{d}{d x} (ln (x x^{2} - 9))

Apply the chain rule:

\frac{1}{x x ^{2} - 9} \frac{d}{d x} (x x^{2} - 9)

= \frac{1}{x x ^{2} - 9} \frac{d}{d x} (x x^{2} - 9)

\frac{d}{d x} (x x^{2} - 9) = \frac{2 x ^{2} - 9}{x ^{2} - 9}

= \frac{1}{x x ^{2} - 9} \cdot \frac{2 x ^{2} - 9}{x ^{2} - 9}

Simplify

\frac{1}{x x ^{2} - 9} \cdot \frac{2 x ^{2} - 9}{x ^{2} - 9} : \frac{2 x ^{2} - 9}{x ( x ^{2} - 9 )}

= \frac{2 x ^{2} - 9}{x ( x ^{2} - 9 )}

Popular Examples

limit as x approaches infinity of 15

x \to \infty lim (15)

derivative of f(x)= x/(sqrt(x)+9)derivative of

f (x) = \frac{x}{x + 9}

integral of x^3(2x^2-3)

\int x^{3} (2 x^{2} - 3) d x

(\partial)/(\partial x)(4xy(-12-x-y))

\frac{\partial}{\partial x} (4 x y (- 12 - x - y))

inverse oflaplace 1/(s(s-1))inverse laplace

\frac{1}{s ( s - 1 )}

Frequently Asked Questions (FAQ)

What is the derivative of ln(xsqrt(x^2-9)) ?
The derivative of ln(xsqrt(x^2-9)) is (2x^2-9)/(x(x^2-9))
What is the first derivative of ln(xsqrt(x^2-9)) ?
The first derivative of ln(xsqrt(x^2-9)) is (2x^2-9)/(x(x^2-9))