What is the derivative of (sqrt(x)-2/(x-4)) ?

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

What is the first derivative of (sqrt(x)-2/(x-4)) ?

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

\int cos (a x) cos (b x) d x

x \to 2 lim (\frac{x ^{2} - a}{x - 2})

2 x^{3} - 3

\frac{\partial}{\partial y} (2 y - 2)

\frac{d}{d x} (e^{x} cos (9 x))

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