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

The derivative of x+4/(x-4) is 1-4/((x-4)^2)

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

The first derivative of x+4/(x-4) is 1-4/((x-4)^2)

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

What is the derivative of x+4/(x-4) ?
The derivative of x+4/(x-4) is 1-4/((x-4)^2)
What is the first derivative of x+4/(x-4) ?
The first derivative of x+4/(x-4) is 1-4/((x-4)^2)