What is the derivative of h(x)=ln(x+sqrt(x^2-7)) ?

The derivative of h(x)=ln(x+sqrt(x^2-7)) is 1/(sqrt(x^2-7))

What is the first derivative of h(x)=ln(x+sqrt(x^2-7)) ?

The first derivative of h(x)=ln(x+sqrt(x^2-7)) is 1/(sqrt(x^2-7))

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derivative of

h (x) = ln (x + x^{2} - 7)

\frac{1}{x ^{2} - 7}

Solution steps

\frac{d}{d x} (ln (x + x^{2} - 7))

Apply the chain rule:

\frac{1}{x + x ^{2} - 7} \frac{d}{d x} (x + x^{2} - 7)

= \frac{1}{x + x ^{2} - 7} \frac{d}{d x} (x + x^{2} - 7)

\frac{d}{d x} (x + x^{2} - 7) = 1 + \frac{x}{x ^{2} - 7}

= \frac{1}{x + x ^{2} - 7} (1 + \frac{x}{x ^{2} - 7})

Simplify

\frac{1}{x + x ^{2} - 7} (1 + \frac{x}{x ^{2} - 7}) : \frac{1}{x ^{2} - 7}

= \frac{1}{x ^{2} - 7}

What is the derivative of h(x)=ln(x+sqrt(x^2-7)) ?
The derivative of h(x)=ln(x+sqrt(x^2-7)) is 1/(sqrt(x^2-7))
What is the first derivative of h(x)=ln(x+sqrt(x^2-7)) ?
The first derivative of h(x)=ln(x+sqrt(x^2-7)) is 1/(sqrt(x^2-7))