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

The derivative of y= x/((x+1)^2) is (1-x)/((x+1)^3)

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

The first derivative of y= x/((x+1)^2) is (1-x)/((x+1)^3)

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

\frac{d}{d q} (\frac{( tan ( q ) )}{( 1 + tan ( q ) )})

(e^{x})^{4}

\frac{1}{( x ^{2} + 4 )}

(x^{2} + 3 x)^{15}

f (x) = cos^{3} (3 x - 1)

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