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

The derivative of ((x+2(x+1))/(2x-1)) is (2x^2-2x-7)/((2x-1)^2)

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

The first derivative of ((x+2(x+1))/(2x-1)) is (2x^2-2x-7)/((2x-1)^2)

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

\frac{2 x ^{2} - 2 x - 7}{( 2 x - 1 ) ^{2}}

Solution steps

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

\frac{d}{d x} ((x + 2) (x + 1)) = 2 x + 3

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

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

Expand

(2 x + 3) (2 x - 1) - 2 (x + 2) (x + 1) : 2 x^{2} - 2 x - 7

= \frac{2 x ^{2} - 2 x - 7}{( 2 x - 1 ) ^{2}}

\int_{0}^{\infty} u^{2} e^{- u} d u

\frac{\partial}{\partial y} (z - x^{2} + y^{2})

d er i v a t i v e - 3 e^{x^{5}}

\int \frac{( x - 1 )}{( x + 1 )} d x

\int \frac{2}{25 - 2 x ^{2}} d x

What is the derivative of ((x+2(x+1))/(2x-1)) ?
The derivative of ((x+2(x+1))/(2x-1)) is (2x^2-2x-7)/((2x-1)^2)
What is the first derivative of ((x+2(x+1))/(2x-1)) ?
The first derivative of ((x+2(x+1))/(2x-1)) is (2x^2-2x-7)/((2x-1)^2)