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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

f (x) = 2 x - 5 x, (4, - 2)

h \to 0 lim (3 x^{2} + 2 x h + h^{2})

\int 20 x ln (x) d x

\int (x^{3} e^{4 x}) d x

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

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