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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} + y = 0

f (x) = x^{8} - 46

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

\frac{d}{d x} (2 9^{x})

\int \frac{100}{x ^{3} - 10 x ^{2}} d x

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