What is the derivative of (xcos(x))/(1+x^2) ?

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

What is the first derivative of (xcos(x))/(1+x^2) ?

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

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derivative of

\frac{x cos ( x )}{1 + x ^{2}}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

1 + w^{2}

2 (x sin (x) + cos (x))

\frac{1}{3 x ^{2} + 2}

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

\frac{6}{2 - 4 x}

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