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

The derivative of 1/2 x^4-2x^2 is 2x^3-4x

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

The first derivative of 1/2 x^4-2x^2 is 2x^3-4x

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

2 x^{3} - 4 x

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= 2 x^{3} - 4 x

What is the derivative of 1/2 x^4-2x^2 ?
The derivative of 1/2 x^4-2x^2 is 2x^3-4x
What is the first derivative of 1/2 x^4-2x^2 ?
The first derivative of 1/2 x^4-2x^2 is 2x^3-4x