What is the derivative of (m+2)/(m^2+5m+6) ?

The derivative of (m+2)/(m^2+5m+6) is (-m^2-4m-4)/((m^2+5m+6)^2)

What is the first derivative of (m+2)/(m^2+5m+6) ?

The first derivative of (m+2)/(m^2+5m+6) is (-m^2-4m-4)/((m^2+5m+6)^2)

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derivative of

\frac{m + 2}{m ^{2} + 5 m + 6}

\frac{- m ^{2} - 4 m - 4}{( m ^{2} + 5 m + 6 ) ^{2}}

Solution steps

\frac{d}{d m} (\frac{m + 2}{m ^{2} + 5 m + 6})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d m} ( m + 2 ) ( m ^{2} + 5 m + 6 ) - \frac{d}{d m} ( m ^{2} + 5 m + 6 ) ( m + 2 )}{( m ^{2} + 5 m + 6 ) ^{2}}

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

\frac{d}{d m} (m^{2} + 5 m + 6) = 2 m + 5

= \frac{1 \cdot ( m ^{2} + 5 m + 6 ) - ( 2 m + 5 ) ( m + 2 )}{( m ^{2} + 5 m + 6 ) ^{2}}

Simplify

\frac{1 \cdot ( m ^{2} + 5 m + 6 ) - ( 2 m + 5 ) ( m + 2 )}{( m ^{2} + 5 m + 6 ) ^{2}} : \frac{- m ^{2} - 4 m - 4}{( m ^{2} + 5 m + 6 ) ^{2}}

= \frac{- m ^{2} - 4 m - 4}{( m ^{2} + 5 m + 6 ) ^{2}}

\frac{\partial}{\partial z} (\frac{( x - y )}{z})

\int (3 t^{2} - 4 t + 5) d t

\int sin^{4} (x) cos^{2} (d) x d x

\frac{\partial}{\partial y} ((1 + x y)^{\frac{3}{2}})

\int \frac{cos ( x )}{cos ^{2} ( x )} d x

What is the derivative of (m+2)/(m^2+5m+6) ?
The derivative of (m+2)/(m^2+5m+6) is (-m^2-4m-4)/((m^2+5m+6)^2)
What is the first derivative of (m+2)/(m^2+5m+6) ?
The first derivative of (m+2)/(m^2+5m+6) is (-m^2-4m-4)/((m^2+5m+6)^2)