What is the derivative of (24x^2+36x)/(2x+2) ?

The derivative of (24x^2+36x)/(2x+2) is (6(2x^2+4x+3))/((x+1)^2)

What is the first derivative of (24x^2+36x)/(2x+2) ?

The first derivative of (24x^2+36x)/(2x+2) is (6(2x^2+4x+3))/((x+1)^2)

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derivative of

\frac{24 x ^{2} + 36 x}{2 x + 2}

\frac{6 ( 2 x ^{2} + 4 x + 3 )}{( x + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{24 x ^{2} + 36 x}{2 x + 2})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 24 x ^{2} + 36 x ) ( 2 x + 2 ) - \frac{d}{d x} ( 2 x + 2 ) ( 24 x ^{2} + 36 x )}{( 2 x + 2 ) ^{2}}

\frac{d}{d x} (24 x^{2} + 36 x) = 48 x + 36

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

= \frac{( 48 x + 36 ) ( 2 x + 2 ) - 2 ( 24 x ^{2} + 36 x )}{( 2 x + 2 ) ^{2}}

Simplify

\frac{( 48 x + 36 ) ( 2 x + 2 ) - 2 ( 24 x ^{2} + 36 x )}{( 2 x + 2 ) ^{2}} : \frac{6 ( 2 x ^{2} + 4 x + 3 )}{( x + 1 ) ^{2}}

= \frac{6 ( 2 x ^{2} + 4 x + 3 )}{( x + 1 ) ^{2}}

What is the derivative of (24x^2+36x)/(2x+2) ?
The derivative of (24x^2+36x)/(2x+2) is (6(2x^2+4x+3))/((x+1)^2)
What is the first derivative of (24x^2+36x)/(2x+2) ?
The first derivative of (24x^2+36x)/(2x+2) is (6(2x^2+4x+3))/((x+1)^2)