What is the derivative of 9/2 x^2 ?

The derivative of 9/2 x^2 is 9x

What is the first derivative of 9/2 x^2 ?

The first derivative of 9/2 x^2 is 9x

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\frac{d}{d x} (\frac{9}{2} x^{2})

9 x

Solution steps

\frac{d}{d x} (\frac{9}{2} x^{2})

Take the constant out:

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

= \frac{9}{2} \frac{d}{d x} (x^{2})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{9}{2} \cdot 2 x^{2 - 1}

Simplify

\frac{9}{2} \cdot 2 x^{2 - 1} : 9 x

= 9 x