What is the derivative of sqrt(x^2-5) ?

The derivative of sqrt(x^2-5) is x/(sqrt(x^2-5))

What is the first derivative of sqrt(x^2-5) ?

The first derivative of sqrt(x^2-5) is x/(sqrt(x^2-5))

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\frac{d}{d x} (x^{2} - 5)

\frac{x}{x ^{2} - 5}

Solution steps

\frac{d}{d x} (x^{2} - 5)

Apply the chain rule:

\frac{1}{2 x ^{2} - 5} \frac{d}{d x} (x^{2} - 5)

= \frac{1}{2 x ^{2} - 5} \frac{d}{d x} (x^{2} - 5)

\frac{d}{d x} (x^{2} - 5) = 2 x

= \frac{1}{2 x ^{2} - 5} \cdot 2 x

Simplify

\frac{1}{2 x ^{2} - 5} \cdot 2 x : \frac{x}{x ^{2} - 5}

= \frac{x}{x ^{2} - 5}

What is the derivative of sqrt(x^2-5) ?
The derivative of sqrt(x^2-5) is x/(sqrt(x^2-5))
What is the first derivative of sqrt(x^2-5) ?
The first derivative of sqrt(x^2-5) is x/(sqrt(x^2-5))