What is the derivative of ((5+sqrt(4-x))/6) ?

The derivative of ((5+sqrt(4-x))/6) is -1/(12sqrt(-x+4))

What is the first derivative of ((5+sqrt(4-x))/6) ?

The first derivative of ((5+sqrt(4-x))/6) is -1/(12sqrt(-x+4))

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\frac{d}{d x} (\frac{( 5 + 4 - x )}{6})

- \frac{1}{12 - x + 4}

Solution steps

\frac{d}{d x} (\frac{( 5 + 4 - x )}{6})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{6} \frac{d}{d x} (5 + 4 - x)

Apply the Sum/Difference Rule:

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

= \frac{1}{6} (\frac{d}{d x} (5) + \frac{d}{d x} (4 - x))

\frac{d}{d x} (5) = 0

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

= \frac{1}{6} (0 - \frac{1}{2 4 - x})

Simplify

\frac{1}{6} (0 - \frac{1}{2 4 - x}) : - \frac{1}{12 - x + 4}

= - \frac{1}{12 - x + 4}

What is the derivative of ((5+sqrt(4-x))/6) ?
The derivative of ((5+sqrt(4-x))/6) is -1/(12sqrt(-x+4))
What is the first derivative of ((5+sqrt(4-x))/6) ?
The first derivative of ((5+sqrt(4-x))/6) is -1/(12sqrt(-x+4))