What is the derivative of (9x)/(3x+7) ?

The derivative of (9x)/(3x+7) is (63)/((3x+7)^2)

What is the first derivative of (9x)/(3x+7) ?

The first derivative of (9x)/(3x+7) is (63)/((3x+7)^2)

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derivative of

\frac{9 x}{3 x + 7}

\frac{63}{( 3 x + 7 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{9 x}{3 x + 7})

Take the constant out:

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

= 9 \frac{d}{d x} (\frac{x}{3 x + 7})

Apply the Quotient Rule:

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

= 9 \cdot \frac{\frac{d x}{d x} ( 3 x + 7 ) - \frac{d}{d x} ( 3 x + 7 ) x}{( 3 x + 7 ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (3 x + 7) = 3

= 9 \cdot \frac{1 \cdot ( 3 x + 7 ) - 3 x}{( 3 x + 7 ) ^{2}}

Simplify

9 \cdot \frac{1 \cdot ( 3 x + 7 ) - 3 x}{( 3 x + 7 ) ^{2}} : \frac{63}{( 3 x + 7 ) ^{2}}

= \frac{63}{( 3 x + 7 ) ^{2}}

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What is the derivative of (9x)/(3x+7) ?
The derivative of (9x)/(3x+7) is (63)/((3x+7)^2)
What is the first derivative of (9x)/(3x+7) ?
The first derivative of (9x)/(3x+7) is (63)/((3x+7)^2)