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

The derivative of ln(x+sqrt(x^2-10)) is 1/(sqrt(x^2-10))

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

The first derivative of ln(x+sqrt(x^2-10)) is 1/(sqrt(x^2-10))

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derivative of

ln (x + x^{2} - 10)

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

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

Simplify

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

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

sin (9 x)

\frac{d}{d x} (x + 1 - x)

\frac{d}{d θ} (3 tan (θ))

n = 1 \sum \infty a^{n - 1} \cdot n

\int sin (x + 5) d x

What is the derivative of ln(x+sqrt(x^2-10)) ?
The derivative of ln(x+sqrt(x^2-10)) is 1/(sqrt(x^2-10))
What is the first derivative of ln(x+sqrt(x^2-10)) ?
The first derivative of ln(x+sqrt(x^2-10)) is 1/(sqrt(x^2-10))