What is the derivative of (x^2+9)/(x+3) ?

The derivative of (x^2+9)/(x+3) is (x^2+6x-9)/((x+3)^2)

What is the first derivative of (x^2+9)/(x+3) ?

The first derivative of (x^2+9)/(x+3) is (x^2+6x-9)/((x+3)^2)

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derivative of

\frac{x ^{2} + 9}{x + 3}

\frac{x ^{2} + 6 x - 9}{( x + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 9}{x + 3})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{2} + 9 ) ( x + 3 ) - \frac{d}{d x} ( x + 3 ) ( x ^{2} + 9 )}{( x + 3 ) ^{2}}

\frac{d}{d x} (x^{2} + 9) = 2 x

\frac{d}{d x} (x + 3) = 1

= \frac{2 x ( x + 3 ) - 1 \cdot ( x ^{2} + 9 )}{( x + 3 ) ^{2}}

Simplify

\frac{2 x ( x + 3 ) - 1 \cdot ( x ^{2} + 9 )}{( x + 3 ) ^{2}} : \frac{x ^{2} + 6 x - 9}{( x + 3 ) ^{2}}

= \frac{x ^{2} + 6 x - 9}{( x + 3 ) ^{2}}

What is the derivative of (x^2+9)/(x+3) ?
The derivative of (x^2+9)/(x+3) is (x^2+6x-9)/((x+3)^2)
What is the first derivative of (x^2+9)/(x+3) ?
The first derivative of (x^2+9)/(x+3) is (x^2+6x-9)/((x+3)^2)