What is the derivative of (x-a/(b-a)) ?

The derivative of (x-a/(b-a)) is 1/(b-a)

What is the first derivative of (x-a/(b-a)) ?

The first derivative of (x-a/(b-a)) is 1/(b-a)

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\frac{d}{d x} (\frac{x - a}{b - a})

\frac{1}{b - a}

Solution steps

\frac{d}{d x} (\frac{x - a}{b - a})

Take the constant out:

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

= \frac{1}{b - a} \frac{d}{d x} (x - a)

Apply the Sum/Difference Rule:

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

= \frac{1}{b - a} (\frac{d x}{d x} - \frac{d a}{d x})

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

\frac{d a}{d x} = 0

= \frac{1}{b - a} (1 - 0)

Simplify

= \frac{1}{b - a}

What is the derivative of (x-a/(b-a)) ?
The derivative of (x-a/(b-a)) is 1/(b-a)
What is the first derivative of (x-a/(b-a)) ?
The first derivative of (x-a/(b-a)) is 1/(b-a)