What is the derivative of y=4x^3(2-3x) ?

The derivative of y=4x^3(2-3x) is 4(6x^2-12x^3)

What is the first derivative of y=4x^3(2-3x) ?

The first derivative of y=4x^3(2-3x) is 4(6x^2-12x^3)

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derivative of

y = 4 x^{3} (2 - 3 x)

4 (6 x^{2} - 12 x^{3})

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

4 (3 x^{2} (2 - 3 x) + (- 3) x^{3}) : 4 (6 x^{2} - 12 x^{3})

= 4 (6 x^{2} - 12 x^{3})

What is the derivative of y=4x^3(2-3x) ?
The derivative of y=4x^3(2-3x) is 4(6x^2-12x^3)
What is the first derivative of y=4x^3(2-3x) ?
The first derivative of y=4x^3(2-3x) is 4(6x^2-12x^3)