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

The derivative of B(x-2)^2x^2 is B(4x^3-12x^2+8x)

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

The first derivative of B(x-2)^2x^2 is B(4x^3-12x^2+8x)

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derivative of

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

B (4 x^{3} - 12 x^{2} + 8 x)

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Expand

2 (x - 2) x^{2} + 2 x (x - 2)^{2} : 4 x^{3} - 12 x^{2} + 8 x

= B (4 x^{3} - 12 x^{2} + 8 x)

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What is the derivative of B(x-2)^2x^2 ?
The derivative of B(x-2)^2x^2 is B(4x^3-12x^2+8x)
What is the first derivative of B(x-2)^2x^2 ?
The first derivative of B(x-2)^2x^2 is B(4x^3-12x^2+8x)