What is the derivative of (4x+2/(x+1)) ?

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

What is the first derivative of (4x+2/(x+1)) ?

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

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

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

Solution steps

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

\frac{d}{d x} (4 x + 2) = 4

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

= \frac{4 ( x + 1 ) - 1 \cdot ( 4 x + 2 )}{( x + 1 ) ^{2}}

Simplify

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

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

\int tan^{5} (5 x) d x

\int \frac{e}{x} + \frac{x}{e} d x

\int sec^{2} (x) cos (x) d x

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

\frac{d}{d x} (ln (x^{4} + 27))

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