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

The derivative of ((x+1)(x-2))/(x^2) is (x+4)/(x^3)

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

The first derivative of ((x+1)(x-2))/(x^2) is (x+4)/(x^3)

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derivative of

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

\frac{x + 4}{x ^{3}}

Solution steps

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

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

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

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

Simplify

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

= \frac{x + 4}{x ^{3}}

(- 1 + 2 t)^{- 1}

y = x^{3} + 2 x - 1

a^{\frac{1}{x}}

3 ln (2 x - 1)

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

What is the derivative of ((x+1)(x-2))/(x^2) ?
The derivative of ((x+1)(x-2))/(x^2) is (x+4)/(x^3)
What is the first derivative of ((x+1)(x-2))/(x^2) ?
The first derivative of ((x+1)(x-2))/(x^2) is (x+4)/(x^3)