What is the derivative of x^3(4x^2-5x-6) ?

The derivative of x^3(4x^2-5x-6) is 20x^4-20x^3-18x^2

What is the first derivative of x^3(4x^2-5x-6) ?

The first derivative of x^3(4x^2-5x-6) is 20x^4-20x^3-18x^2

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\frac{d}{d x} (x^{3} (4 x^{2} - 5 x - 6))

20 x^{4} - 20 x^{3} - 18 x^{2}

Solution steps

\frac{d}{d x} (x^{3} (4 x^{2} - 5 x - 6))

Apply the Product Rule:

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

f = x^{3}, g = 4 x^{2} - 5 x - 6

= \frac{d}{d x} (x^{3}) (4 x^{2} - 5 x - 6) + \frac{d}{d x} (4 x^{2} - 5 x - 6) x^{3}

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

\frac{d}{d x} (4 x^{2} - 5 x - 6) = 8 x - 5

= 3 x^{2} (4 x^{2} - 5 x - 6) + (8 x - 5) x^{3}

Simplify

3 x^{2} (4 x^{2} - 5 x - 6) + (8 x - 5) x^{3} : 20 x^{4} - 20 x^{3} - 18 x^{2}

= 20 x^{4} - 20 x^{3} - 18 x^{2}

What is the derivative of x^3(4x^2-5x-6) ?
The derivative of x^3(4x^2-5x-6) is 20x^4-20x^3-18x^2
What is the first derivative of x^3(4x^2-5x-6) ?
The first derivative of x^3(4x^2-5x-6) is 20x^4-20x^3-18x^2