What is the derivative of (sqrt(x))/(4x+8) ?

The derivative of (sqrt(x))/(4x+8) is -(x-2)/(8sqrt(x)(x+2)^2)

What is the first derivative of (sqrt(x))/(4x+8) ?

The first derivative of (sqrt(x))/(4x+8) is -(x-2)/(8sqrt(x)(x+2)^2)

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derivative of

\frac{x}{4 x + 8}

- \frac{x - 2}{8 x ( x + 2 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{4 x + 8})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ) ( 4 x + 8 ) - \frac{d}{d x} ( 4 x + 8 ) x}{( 4 x + 8 ) ^{2}}

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

\frac{d}{d x} (4 x + 8) = 4

= \frac{\frac{1}{2 x} ( 4 x + 8 ) - 4 x}{( 4 x + 8 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( 4 x + 8 ) - 4 x}{( 4 x + 8 ) ^{2}} : - \frac{x - 2}{8 x ( x + 2 ) ^{2}}

= - \frac{x - 2}{8 x ( x + 2 ) ^{2}}

(x^{2} - 9) \frac{d y}{d x} + 6 y = (x + 3)^{2}

x \to 1 + lim (\frac{x - 4}{1 - x})

\frac{\partial}{\partial x} (e^{x - 1})

5 e^{3 t}

What is the derivative of (sqrt(x))/(4x+8) ?
The derivative of (sqrt(x))/(4x+8) is -(x-2)/(8sqrt(x)(x+2)^2)
What is the first derivative of (sqrt(x))/(4x+8) ?
The first derivative of (sqrt(x))/(4x+8) is -(x-2)/(8sqrt(x)(x+2)^2)