What is the derivative of sqrt(x^2-1) ?

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

What is the first derivative of sqrt(x^2-1) ?

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

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derivative of

x^{2} - 1

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d y}{d x} = 4 x e^{2 x}

\frac{\partial}{\partial x} (x + ln (5 x + y))

\int 5 x + 1 d x

2 x^{2} + x - 1, at x = 1

\int \frac{x ^{2}}{( 10 - x ) ( 10 + x )} d x

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