What is the derivative of y=ln(x+sqrt(x^2-6)) ?

The derivative of y=ln(x+sqrt(x^2-6)) is 1/(sqrt(x^2-6))

What is the first derivative of y=ln(x+sqrt(x^2-6)) ?

The first derivative of y=ln(x+sqrt(x^2-6)) is 1/(sqrt(x^2-6))

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derivative of

y = ln (x + x^{2} - 6)

\frac{1}{x ^{2} - 6}

Solution steps

\frac{d}{d x} (ln (x + x^{2} - 6))

Apply the chain rule:

\frac{1}{x + x ^{2} - 6} \frac{d}{d x} (x + x^{2} - 6)

= \frac{1}{x + x ^{2} - 6} \frac{d}{d x} (x + x^{2} - 6)

\frac{d}{d x} (x + x^{2} - 6) = 1 + \frac{x}{x ^{2} - 6}

= \frac{1}{x + x ^{2} - 6} (1 + \frac{x}{x ^{2} - 6})

Simplify

\frac{1}{x + x ^{2} - 6} (1 + \frac{x}{x ^{2} - 6}) : \frac{1}{x ^{2} - 6}

= \frac{1}{x ^{2} - 6}

What is the derivative of y=ln(x+sqrt(x^2-6)) ?
The derivative of y=ln(x+sqrt(x^2-6)) is 1/(sqrt(x^2-6))
What is the first derivative of y=ln(x+sqrt(x^2-6)) ?
The first derivative of y=ln(x+sqrt(x^2-6)) is 1/(sqrt(x^2-6))