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

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

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

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

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derivative of

\frac{x}{x + 9}

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

n = 4 \sum \infty (\frac{1}{2})^{n}

\int \frac{1}{- e ^{3 x}} d x

\int_{0}^{\infty} \frac{1}{e ^{x}} d x

\frac{d}{d x} (2 e^{4 x} + x)

\frac{d}{d x} (2 e^{x} - 3 x^{2} x)

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