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

The derivative of (x^2/(sqrt(x^2-1))) is (x^3-2x)/((x^2-1)sqrt(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 (x^3-2x)/((x^2-1)sqrt(x^2-1))

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

\frac{x ^{3} - 2 x}{( x ^{2} - 1 ) x ^{2} - 1}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

\frac{2 x x ^{2} - 1 - \frac{x}{x ^{2} - 1} x ^{2}}{( x ^{2} - 1 ) ^{2}} : \frac{x ^{3} - 2 x}{( x ^{2} - 1 ) x ^{2} - 1}

= \frac{x ^{3} - 2 x}{( x ^{2} - 1 ) x ^{2} - 1}

\frac{7 + 2 x}{5 - 8 x}

\frac{\partial}{\partial x} (\frac{1}{tan ( x y )})

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

\frac{\partial}{\partial x} (e^{- 2 x} \cdot cos (2 y))

\int \frac{5 x - 3}{x ^{2} - 1} d x

What is the derivative of (x^2/(sqrt(x^2-1))) ?
The derivative of (x^2/(sqrt(x^2-1))) is (x^3-2x)/((x^2-1)sqrt(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 (x^3-2x)/((x^2-1)sqrt(x^2-1))