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

The derivative of (x^4/2) is 2x^3

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

The first derivative of (x^4/2) is 2x^3

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

2 x^{3}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

= \frac{1}{2} \cdot 4 x^{4 - 1}

Simplify

\frac{1}{2} \cdot 4 x^{4 - 1} : 2 x^{3}

= 2 x^{3}

\int_{- 1}^{4} (x + 3) d x

\frac{d}{d x} (- 7 e^{x})

\frac{d}{d s} (\frac{6}{( s - 2 ) ^{2} + 36})

\int \frac{1}{x ^{5} + x ^{4} + 2 x ^{3} + 2 x ^{2} + x + 1} d x

2 cos (t - \frac{π}{6})

What is the derivative of (x^4/2) ?
The derivative of (x^4/2) is 2x^3
What is the first derivative of (x^4/2) ?
The first derivative of (x^4/2) is 2x^3