What is the derivative of (x^3-1/2) ?

The derivative of (x^3-1/2) is (3x^2)/2

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

The first derivative of (x^3-1/2) is (3x^2)/2

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

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

Solution steps

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

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= \frac{1}{2} (3 x^{2} - 0)

Simplify

\frac{1}{2} (3 x^{2} - 0) : \frac{3 x ^{2}}{2}

= \frac{3 x ^{2}}{2}

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