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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

x \to \infty lim (0. 3^{x})

f (x) = \frac{sin ( x )}{5 + 5 cos ( x )}, at x = \frac{π}{3}

\frac{s + 1}{s ^{2} + 2 s + s}

\frac{\partial}{\partial x} (\frac{6 x}{y})

\int sin (π y) d y

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