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Popular >

derivative of f(x)=ln(sqrt(x^2-9))

Solution

derivative of

f (x) = ln (x^{2} - 9)

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

inverse oflaplace sin^2(+t)inverse laplace

sin^{2} (+ t)

derivative of sqrt(-x)

\frac{d}{d x} (- x)

(\partial)/(\partial x)(e^{xy}ln(z))

\frac{\partial}{\partial x} (e^{x y} ln (z))

integral of t^2cos(t^3)

\int t^{2} cos (t^{3}) d t

limit as x approaches 0 of (|x|)/x-1

x \to 0 lim (\frac{∣ x ∣}{x} - 1)

Frequently Asked Questions (FAQ)

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