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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{d}{d t} (2 t^{4})

\int 3 x^{\frac{1}{2}} d x

d er i v a t i v e f (x) 50 - x

\int \frac{1}{( 1 + 4 x ^{2} )} d x

\frac{d x}{d t} - 3 x = cos (4 t)

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