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

The derivative of ((x-1^2)/((x+2))) is (x^2+4x-5)/((x+2)^2)

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

The first derivative of ((x-1^2)/((x+2))) is (x^2+4x-5)/((x+2)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{2 ( x - 1 ) ( x + 2 ) - 1 \cdot ( x - 1 ) ^{2}}{( x + 2 ) ^{2}} : \frac{x ^{2} + 4 x - 5}{( x + 2 ) ^{2}}

= \frac{x ^{2} + 4 x - 5}{( x + 2 ) ^{2}}

\frac{d}{d v} (v^{2})

\int 8 x^{3} (1 + x^{4})^{10} d x

\int \frac{1}{( x ^{2} x ^{2} - 16 )} d x

f (x) = 9 x^{\frac{1}{2}} + x^{\frac{3}{2}}, at x = 9

\frac{d}{d x} (\frac{7}{4 x})

What is the derivative of ((x-1^2)/((x+2))) ?
The derivative of ((x-1^2)/((x+2))) is (x^2+4x-5)/((x+2)^2)
What is the first derivative of ((x-1^2)/((x+2))) ?
The first derivative of ((x-1^2)/((x+2))) is (x^2+4x-5)/((x+2)^2)