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

The derivative of x^2(4-x)^2 is 4x^3-24x^2+32x

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

The first derivative of x^2(4-x)^2 is 4x^3-24x^2+32x

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derivative of

x^{2} (4 - x)^{2}

4 x^{3} - 24 x^{2} + 32 x

Solution steps

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

Apply the Product Rule:

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

f = x^{2}, g = (4 - x)^{2}

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

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

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

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

Simplify

2 x (4 - x)^{2} + (- 2 (4 - x)) x^{2} : 4 x^{3} - 24 x^{2} + 32 x

= 4 x^{3} - 24 x^{2} + 32 x

What is the derivative of x^2(4-x)^2 ?
The derivative of x^2(4-x)^2 is 4x^3-24x^2+32x
What is the first derivative of x^2(4-x)^2 ?
The first derivative of x^2(4-x)^2 is 4x^3-24x^2+32x