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})

Simplify

\frac{- 2}{2 x + 5} : - \frac{2}{2 x + 5}

= \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}}

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

\frac{d y}{d t} + e^{t} y = - 24 e^{t}

\int 3^{x + 2} d x

(sin (x) + cos (x))^{^{'}}

\int \frac{( x + sin ( x ) )}{( 1 + cos ( x ) )} 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)