What is the derivative of (x^2+3x-4/(x+2)) ?

The derivative of (x^2+3x-4/(x+2)) is (x^2+4x+10)/((x+2)^2)

What is the first derivative of (x^2+3x-4/(x+2)) ?

The first derivative of (x^2+3x-4/(x+2)) is (x^2+4x+10)/((x+2)^2)

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\frac{d}{d x} (\frac{x ^{2} + 3 x - 4}{x + 2})

\frac{x ^{2} + 4 x + 10}{( x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 3 x - 4}{x + 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + 3 x - 4 ) ( x + 2 ) - \frac{d}{d x} ( x + 2 ) ( x ^{2} + 3 x - 4 )}{( x + 2 ) ^{2}}

\frac{d}{d x} (x^{2} + 3 x - 4) = 2 x + 3

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

= \frac{( 2 x + 3 ) ( x + 2 ) - 1 \cdot ( x ^{2} + 3 x - 4 )}{( x + 2 ) ^{2}}

Simplify

\frac{( 2 x + 3 ) ( x + 2 ) - 1 \cdot ( x ^{2} + 3 x - 4 )}{( x + 2 ) ^{2}} : \frac{x ^{2} + 4 x + 10}{( x + 2 ) ^{2}}

= \frac{x ^{2} + 4 x + 10}{( x + 2 ) ^{2}}

\frac{d}{d x} (\frac{a + b x ^{2}}{x ^{2}})

\frac{d}{d x} (\frac{( x ^{4} )}{12} + \frac{( x ^{3} )}{3})

\int_{1}^{e} 4 t^{2} ln (t) d t

x \to 0 lim (tan^{x} (5 x))

4 x^{2} - 5 x + 1

What is the derivative of (x^2+3x-4/(x+2)) ?
The derivative of (x^2+3x-4/(x+2)) is (x^2+4x+10)/((x+2)^2)
What is the first derivative of (x^2+3x-4/(x+2)) ?
The first derivative of (x^2+3x-4/(x+2)) is (x^2+4x+10)/((x+2)^2)