What is the derivative of f(x)=(1-|x^3|)+(1-x^3) ?

The derivative of f(x)=(1-|x^3|)+(1-x^3) is -(3x^5)/(|x^3|)-3x^2

What is the first derivative of f(x)=(1-|x^3|)+(1-x^3) ?

The first derivative of f(x)=(1-|x^3|)+(1-x^3) is -(3x^5)/(|x^3|)-3x^2

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derivative of

f (x) = (1 - x^{3}) + (1 - x^{3})

- \frac{3 x ^{5}}{∣ x ^{3} ∣} - 3 x^{2}

Solution steps

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

Simplify

(1 - x^{3}) + 1 - x^{3} : - x^{3} - x^{3} + 2

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

Apply the Sum/Difference Rule:

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

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

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

\frac{d}{d x} (x^{3}) = \frac{3 x ^{5}}{∣ x ^{3} ∣}

\frac{d}{d x} (2) = 0

= - 3 x^{2} - \frac{3 x ^{5}}{∣ x ^{3} ∣} + 0

Simplify

= - \frac{3 x ^{5}}{∣ x ^{3} ∣} - 3 x^{2}

What is the derivative of f(x)=(1-|x^3|)+(1-x^3) ?
The derivative of f(x)=(1-|x^3|)+(1-x^3) is -(3x^5)/(|x^3|)-3x^2
What is the first derivative of f(x)=(1-|x^3|)+(1-x^3) ?
The first derivative of f(x)=(1-|x^3|)+(1-x^3) is -(3x^5)/(|x^3|)-3x^2