What is the derivative of (2x-5/(2x+5)) ?

The derivative of (2x-5/(2x+5)) is (20)/((2x+5)^2)

What is the first derivative of (2x-5/(2x+5)) ?

The first derivative of (2x-5/(2x+5)) is (20)/((2x+5)^2)

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\frac{d}{d x} (\frac{2 x - 5}{2 x + 5})

\frac{20}{( 2 x + 5 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x - 5}{2 x + 5})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (2 x - 5) = 2

\frac{d}{d x} (2 x + 5) = 2

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

Expand

2 (2 x + 5) - 2 (2 x - 5) : 20

= \frac{20}{( 2 x + 5 ) ^{2}}

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

\int - 5 x e^{x^{2}} d x

\int cos (7 x) cos (3 x) d x

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

x^{2} \cdot ln (7 x)

What is the derivative of (2x-5/(2x+5)) ?
The derivative of (2x-5/(2x+5)) is (20)/((2x+5)^2)
What is the first derivative of (2x-5/(2x+5)) ?
The first derivative of (2x-5/(2x+5)) is (20)/((2x+5)^2)