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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

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