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

The derivative of (xsin(x)/(x^2-1)) is (x^3cos(x)-x^2sin(x)-xcos(x)-sin(x))/((x^2-1)^2)

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

The first derivative of (xsin(x)/(x^2-1)) is (x^3cos(x)-x^2sin(x)-xcos(x)-sin(x))/((x^2-1)^2)

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

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

Solution steps

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

\frac{d}{d x} (x sin (x)) = sin (x) + x cos (x)

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

= \frac{( sin ( x ) + x cos ( x ) ) ( x ^{2} - 1 ) - 2 xx sin ( x )}{( x ^{2} - 1 ) ^{2}}

Simplify

\frac{( sin ( x ) + x cos ( x ) ) ( x ^{2} - 1 ) - 2 xx sin ( x )}{( x ^{2} - 1 ) ^{2}} : \frac{x ^{3} cos ( x ) - x ^{2} sin ( x ) - x cos ( x ) - sin ( x )}{( x ^{2} - 1 ) ^{2}}

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

\int p (p + 4)^{5} d p

\frac{d}{d x} (\frac{e ^{x}}{5 + e ^{x}})

\frac{\partial}{\partial y} (2 x - 5 y + 3)

\int (1 + e^{x} y + x e^{x} y) d x

\int_{1}^{\infty} x e^{- 2 x} d x

What is the derivative of (xsin(x)/(x^2-1)) ?
The derivative of (xsin(x)/(x^2-1)) is (x^3cos(x)-x^2sin(x)-xcos(x)-sin(x))/((x^2-1)^2)
What is the first derivative of (xsin(x)/(x^2-1)) ?
The first derivative of (xsin(x)/(x^2-1)) is (x^3cos(x)-x^2sin(x)-xcos(x)-sin(x))/((x^2-1)^2)