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Popular >

derivative of x*sqrt(x^2-1)

Solution

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

Solution

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

Solution steps

\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{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}

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

Simplify

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

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

Popular Examples

derivative of 1/(log_{10(x)})

\frac{d}{d x} (\frac{1}{lo g _{10} ( x )})

(\partial)/(\partial y)(4x^3y^3-1)

\frac{\partial}{\partial y} (4 x^{3} y^{3} - 1)

integral of (4+x+x^2)/(sqrt(x))

\int \frac{4 + x + x ^{2}}{x} d x

y^'=-y/(100),y(0)=80

y^{^{'}} = - \frac{y}{100}, y (0) = 80

derivative of 2/(cos(x))

\frac{d}{d x} (\frac{2}{cos ( x )})

Frequently Asked Questions (FAQ)

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