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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = x^{2} - 1

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\frac{d}{d x} (x^{4} - 3 x^{2} + 4)

\frac{d}{d x} (\frac{6 x}{3 - cot ( x )})

x \to 0 lim (x^{3} - 1)

\int_{1}^{4} - 9 x ln (x) d x

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