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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

ln (1 + 4 x)

\int \frac{3 x}{1 - x} d x

\int \frac{( x ^{2} - 4 ) ^{\frac{5}{2}}}{x} d x

x \to 0 lim (\frac{1}{2 x})

\int \frac{1}{( 5 - 4 x - x ^{2} ) ^{\frac{3}{2}}} d x

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