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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

f (x) = x^{2} + 10

\int sin^{2} (\frac{x}{4}) d x

y^{^{'}} + x y = x y^{- 1}

\frac{d}{d x} (x ey (x)^{2} + y ln (x))

\int \frac{1}{x ^{4} 1 + x ^{2}} d x

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