What is the first derivative of 2(x-3) ?

The first derivative of 2(x-3) is 2

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derivative of 2(x-3)

\frac{d}{d x} (2 (x - 3))

2

Solution steps

\frac{d}{d x} (2 (x - 3))

Take the constant out:

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

= 2 \frac{d}{d x} (x - 3)

Apply the Sum/Difference Rule:

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

= 2 (\frac{d x}{d x} - \frac{d}{d x} (3))

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

\frac{d}{d x} (3) = 0

= 2 (1 - 0)

Simplify

= 2

\frac{d y}{d x} = \frac{( x ^{2} y - 32 )}{16 - x ^{2}} + 2

f (x) = \frac{x ^{2}}{x + 5}, at x = 3

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