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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

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