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

The derivative of (2x+1/(x+3)) is 5/((x+3)^2)

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

The first derivative of (2x+1/(x+3)) is 5/((x+3)^2)

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

\frac{5}{( x + 3 ) ^{2}}

Solution steps

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

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

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

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

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

Simplify

\frac{2 ( x + 3 ) - 1 \cdot ( 2 x + 1 )}{( x + 3 ) ^{2}} : \frac{5}{( x + 3 ) ^{2}}

= \frac{5}{( x + 3 ) ^{2}}

\frac{d y}{d t} = t y + t

\frac{d y}{d x} = \frac{1}{2} x + 4

\frac{d y}{d x} + x y = \frac{x}{y ^{3}}

\int \frac{7}{x ^{2} - 6 x + 25} d x

x^{2} + 2 x, 1, 2

What is the derivative of (2x+1/(x+3)) ?
The derivative of (2x+1/(x+3)) is 5/((x+3)^2)
What is the first derivative of (2x+1/(x+3)) ?
The first derivative of (2x+1/(x+3)) is 5/((x+3)^2)