What is (\partial)/(\partial x)(|Ax|^2) ?

The answer to (\partial)/(\partial x)(|Ax|^2) is 2A^2x

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(\partial)/(\partial x)(|Ax|^2)

\frac{\partial}{\partial x} (∣ A x ∣^{2})

2 A^{2} x

Solution steps

\frac{\partial}{\partial x} (∣ A x ∣^{2})

Simplify

∣ A x ∣^{2} : A^{2} x^{2}

= \frac{\partial}{\partial x} (A^{2} x^{2})

Take the constant out:

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

= A^{2} \frac{\partial}{\partial x} (x^{2})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= A^{2} \cdot 2 x^{2 - 1}

Simplify

= 2 A^{2} x

What is (\partial)/(\partial x)(|Ax|^2) ?
The answer to (\partial)/(\partial x)(|Ax|^2) is 2A^2x