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Popular Calculus >

derivative of (x^2+3x/(-6))

Solution

\frac{d}{d x} (\frac{x ^{2} + 3 x}{- 6})

Solution

- \frac{1}{6} (2 x + 3)

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 3 x}{- 6})

Simplify

\frac{x ^{2} + 3 x}{- 6} : - \frac{x ^{2} + 3 x}{6}

= \frac{d}{d x} (- \frac{x ^{2} + 3 x}{6})

Take the constant out:

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

= - \frac{1}{6} \frac{d}{d x} (x^{2} + 3 x)

Apply the Sum/Difference Rule:

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

= - \frac{1}{6} (\frac{d}{d x} (x^{2}) + \frac{d}{d x} (3 x))

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

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

= - \frac{1}{6} (2 x + 3)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (x^2+3x/(-6)) ?
The derivative of (x^2+3x/(-6)) is -1/6 (2x+3)
What is the first derivative of (x^2+3x/(-6)) ?
The first derivative of (x^2+3x/(-6)) is -1/6 (2x+3)