What is the derivative of (((x)sin(x)))/((x+1)) ?

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

What is the first derivative of (((x)sin(x)))/((x+1)) ?

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

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derivative of

\frac{( ( x ) sin ( x ) )}{( x + 1 )}

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

Solution steps

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

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

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

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

Simplify

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

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

y = (2 x - 1) a^{x}

y = 4 x^{3} - 4 x^{2} + x - 1

ln (\frac{( x + 1 )}{( x - 1 )})

\frac{d}{d t} (3 t^{2} + 2 t + 1)

\frac{x ^{2}}{16}

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