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

The derivative of (1/2 x^2-3^2) is x^3-6x

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

The first derivative of (1/2 x^2-3^2) is x^3-6x

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

x^{3} - 6 x

Solution steps

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

Simplify

(\frac{1}{2} x^{2} - 3)^{2} : \frac{x ^{4}}{4} - 3 x^{2} + 9

= \frac{d}{d x} (\frac{x ^{4}}{4} - 3 x^{2} + 9)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{4}}{4}) - \frac{d}{d x} (3 x^{2}) + \frac{d}{d x} (9)

\frac{d}{d x} (\frac{x ^{4}}{4}) = x^{3}

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

\frac{d}{d x} (9) = 0

= x^{3} - 6 x + 0

Simplify

= x^{3} - 6 x

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