What is the derivative of x^2(x^3-1) ?

The derivative of x^2(x^3-1) is 5x^4-2x

What is the first derivative of x^2(x^3-1) ?

The first derivative of x^2(x^3-1) is 5x^4-2x

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derivative of

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

5 x^{4} - 2 x

Solution steps

\frac{d}{d x} (x^{2} (x^{3} - 1))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = x^{3} - 1

= \frac{d}{d x} (x^{2}) (x^{3} - 1) + \frac{d}{d x} (x^{3} - 1) x^{2}

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

\frac{d}{d x} (x^{3} - 1) = 3 x^{2}

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

Simplify

2 x (x^{3} - 1) + 3 x^{2} x^{2} : 5 x^{4} - 2 x

= 5 x^{4} - 2 x

x \to 0 lim (\frac{b - c}{x ^{a}})

4 + 6 x

9

x \to 9 lim (9 x + ∣ x - 9 ∣)

What is the derivative of x^2(x^3-1) ?
The derivative of x^2(x^3-1) is 5x^4-2x
What is the first derivative of x^2(x^3-1) ?
The first derivative of x^2(x^3-1) is 5x^4-2x