What is the derivative of f(x)= 1/6 x^4-6x^2+1 ?

The derivative of f(x)= 1/6 x^4-6x^2+1 is (2x^3)/3-12x

What is the first derivative of f(x)= 1/6 x^4-6x^2+1 ?

The first derivative of f(x)= 1/6 x^4-6x^2+1 is (2x^3)/3-12x

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derivative of

f (x) = \frac{1}{6} x^{4} - 6 x^{2} + 1

\frac{2 x ^{3}}{3} - 12 x

Solution steps

\frac{d}{d x} (\frac{1}{6} x^{4} - 6 x^{2} + 1)

Simplify

\frac{1}{6} x^{4} - 6 x^{2} + 1 : \frac{x ^{4}}{6} - 6 x^{2} + 1

= \frac{d}{d x} (\frac{x ^{4}}{6} - 6 x^{2} + 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{x ^{4}}{6}) - \frac{d}{d x} (6 x^{2}) + \frac{d}{d x} (1)

\frac{d}{d x} (\frac{x ^{4}}{6}) = \frac{2 x ^{3}}{3}

\frac{d}{d x} (6 x^{2}) = 12 x

\frac{d}{d x} (1) = 0

= \frac{2 x ^{3}}{3} - 12 x + 0

Simplify

= \frac{2 x ^{3}}{3} - 12 x

What is the derivative of f(x)= 1/6 x^4-6x^2+1 ?
The derivative of f(x)= 1/6 x^4-6x^2+1 is (2x^3)/3-12x
What is the first derivative of f(x)= 1/6 x^4-6x^2+1 ?
The first derivative of f(x)= 1/6 x^4-6x^2+1 is (2x^3)/3-12x