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

The derivative of (2x-1/(x+3)) is 7/((x+3)^2)

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

The first derivative of (2x-1/(x+3)) is 7/((x+3)^2)

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

\frac{7}{( 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{7}{( x + 3 ) ^{2}}

= \frac{7}{( x + 3 ) ^{2}}

x \to 3 lim (- 2)

\int - 8 x e^{x^{2}} d x

\int sin^{5} (x) cos^{3} (x) d x

\int + e^{8 x} cos (3 x) d x

\frac{d}{d x} (\frac{e ^{x} + e ^{- x}}{7})

What is the derivative of (2x-1/(x+3)) ?
The derivative of (2x-1/(x+3)) is 7/((x+3)^2)
What is the first derivative of (2x-1/(x+3)) ?
The first derivative of (2x-1/(x+3)) is 7/((x+3)^2)