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

The derivative of (sqrt(x)-9/(sqrt(x)+9)) is 9/(sqrt(x)(\sqrt{x)+9)^2}

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

The first derivative of (sqrt(x)-9/(sqrt(x)+9)) is 9/(sqrt(x)(\sqrt{x)+9)^2}

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x - 9) = \frac{1}{2 x}

\frac{d}{d x} (x + 9) = \frac{1}{2 x}

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

Simplify

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

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

(\frac{1}{2}, 1), (3 \frac{3}{4}, 3 \frac{1}{2})

y d x + (x + \frac{2}{y}) d y = 0

\int_{1}^{4} 1 + 9 x d x

d x + e^{7 x} d y = 0

What is the derivative of (sqrt(x)-9/(sqrt(x)+9)) ?
The derivative of (sqrt(x)-9/(sqrt(x)+9)) is 9/(sqrt(x)(\sqrt{x)+9)^2}
What is the first derivative of (sqrt(x)-9/(sqrt(x)+9)) ?
The first derivative of (sqrt(x)-9/(sqrt(x)+9)) is 9/(sqrt(x)(\sqrt{x)+9)^2}