What is the derivative of f(x)=(3x+2)/(x+1) ?

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

What is the first derivative of f(x)=(3x+2)/(x+1) ?

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

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derivative of

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\frac{1}{2} (6 t + 3)^{- \frac{1}{2}}

x^{2} - 7 x - 26, - x^{2} + 3 x + 2

y^{^{'}} = x (x - 1) (x - 5)

\int \frac{y}{1 + x ^{2} y ^{2}} d x

\int \frac{- cos ( n x )}{n} d x

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