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Popular >

derivative of 1/2 x^4-4x^2+4

Solution

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

Solution

2 x^{3} - 8 x

Solution steps

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

Simplify

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (4 x^{2}) = 8 x

\frac{d}{d x} (4) = 0

= 2 x^{3} - 8 x + 0

Simplify

= 2 x^{3} - 8 x

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Frequently Asked Questions (FAQ)

What is the derivative of 1/2 x^4-4x^2+4 ?
The derivative of 1/2 x^4-4x^2+4 is 2x^3-8x
What is the first derivative of 1/2 x^4-4x^2+4 ?
The first derivative of 1/2 x^4-4x^2+4 is 2x^3-8x