What is the derivative of ((x^2+2x-5)/((x+1)^2)) ?

The derivative of ((x^2+2x-5)/((x+1)^2)) is (12)/((x+1)^3)

What is the first derivative of ((x^2+2x-5)/((x+1)^2)) ?

The first derivative of ((x^2+2x-5)/((x+1)^2)) is (12)/((x+1)^3)

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\frac{d}{d x} (\frac{( x ^{2} + 2 x - 5 )}{( x + 1 ) ^{2}})

\frac{12}{( x + 1 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{( x ^{2} + 2 x - 5 )}{( 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} + 2 x - 5 ) ( x + 1 ) ^{2} - \frac{d}{d x} ( ( x + 1 ) ^{2} ) ( x ^{2} + 2 x - 5 )}{( ( x + 1 ) ^{2} ) ^{2}}

\frac{d}{d x} (x^{2} + 2 x - 5) = 2 x + 2

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

= \frac{( 2 x + 2 ) ( x + 1 ) ^{2} - 2 ( x + 1 ) ( x ^{2} + 2 x - 5 )}{( ( x + 1 ) ^{2} ) ^{2}}

Simplify

\frac{( 2 x + 2 ) ( x + 1 ) ^{2} - 2 ( x + 1 ) ( x ^{2} + 2 x - 5 )}{( ( x + 1 ) ^{2} ) ^{2}} : \frac{12}{( x + 1 ) ^{3}}

= \frac{12}{( x + 1 ) ^{3}}

y^{^{''}} - 2 y^{^{'}} + 2 y = 0, y (0) = 0, y^{^{'}} (0) = 1

y = arcsin (\frac{1}{x})

\int 5 ln (x^{2} - x + 12) d x

\int_{2}^{3} \frac{17}{3 - x} d x

\int \frac{1}{x ^{2} 25 - x ^{2}} d (x) d x

What is the derivative of ((x^2+2x-5)/((x+1)^2)) ?
The derivative of ((x^2+2x-5)/((x+1)^2)) is (12)/((x+1)^3)
What is the first derivative of ((x^2+2x-5)/((x+1)^2)) ?
The first derivative of ((x^2+2x-5)/((x+1)^2)) is (12)/((x+1)^3)