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

The derivative of-2/(2x+5) is 4/((2x+5)^2)

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

The first derivative of-2/(2x+5) is 4/((2x+5)^2)

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

\frac{4}{( 2 x + 5 ) ^{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 2 \frac{d}{d x} (\frac{1}{2 x + 5})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= - 2 \frac{d}{d x} ((2 x + 5)^{- 1})

Apply the chain rule:

- \frac{1}{( 2 x + 5 ) ^{2}} \frac{d}{d x} (2 x + 5)

= - \frac{1}{( 2 x + 5 ) ^{2}} \frac{d}{d x} (2 x + 5)

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

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

Simplify

- 2 (- \frac{1}{( 2 x + 5 ) ^{2}} \cdot 2) : \frac{4}{( 2 x + 5 ) ^{2}}

= \frac{4}{( 2 x + 5 ) ^{2}}

f (x) = ln (4 x^{2} + 1)

x \to 1 - lim (\frac{2 x}{x ^{2} - 1})

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

2^{30}

\int sin (\frac{x}{4}) d x

What is the derivative of-2/(2x+5) ?
The derivative of-2/(2x+5) is 4/((2x+5)^2)
What is the first derivative of-2/(2x+5) ?
The first derivative of-2/(2x+5) is 4/((2x+5)^2)