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

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

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

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

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

\frac{9}{( 7 x + 9 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

= \frac{9}{( 7 x + 9 ) ^{2}}

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x y^{^{'}} - 2 y = 6 x^{2}

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