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

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

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

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

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derivative of

\frac{x - 4}{x}

\frac{- x + 8}{2 x ^{2} x - 4}

Solution steps

\frac{d}{d x} (\frac{x - 4}{x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x - 4) = \frac{1}{2 x - 4}

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

= \frac{\frac{1}{2 x - 4} x - 1 \cdot x - 4}{x ^{2}}

Simplify

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

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

f (x) = x^{3} + x - 3

y = 2 sin (3 x)

x \to 0 lim (x cos (\frac{6}{x}))

x \to - 3 + lim (\frac{- 7 x}{x + 3})

\int \frac{x}{4 - 3 x ^{2}} d x

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