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

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

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

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

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

\frac{x}{2}

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (1) = 0

= \frac{x}{2} - 0

Simplify

= \frac{x}{2}

\frac{\partial}{\partial x} (2 x y - 18 x)

\frac{3 x}{x ^{2} + 1}

\frac{d}{d x} (- x^{3} + 2 x + 7)

- \frac{5}{s ^{2} + 2 s + 4}

x^{2} - 2

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