What is (\partial)/(\partial x)(x^'Ax) ?

The answer to (\partial)/(\partial x)(x^'Ax) is ('+1)Ax^'

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(\partial)/(\partial x)(x^'Ax)

\frac{\partial}{\partial x} (x^{^{'}} A x)

(' + 1) A x^{'}

Solution steps

\frac{\partial}{\partial x} (x^{^{'}} A x)

Simplify

x^{^{'}} A x : A x^{^{'} + 1}

= \frac{\partial}{\partial x} (A x^{^{^{'}} + 1})

Take the constant out:

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

= A \frac{\partial}{\partial x} (x^{^{^{'}} + 1})

Apply the Power Rule:

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

= A (^{^{'}} + 1) x^{^{^{'}} + 1 - 1}

Simplify

= (^{^{'}} + 1) A x^{^{^{'}}}

(- 3, 1), (0, - 3)

\int \frac{- x + 2}{3 ( x ^{2} - x + 1 )} d x

\frac{1}{( s - 3 ) ^{4}}

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

What is (\partial)/(\partial x)(x^'Ax) ?
The answer to (\partial)/(\partial x)(x^'Ax) is ('+1)Ax^'