What is (\partial)/(\partial x)((z)(x^2+y^2+xy)) ?

The answer to (\partial)/(\partial x)((z)(x^2+y^2+xy)) is z(2x+y)

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(\partial)/(\partial x)((z)(x^2+y^2+xy))

\frac{\partial}{\partial x} ((z) (x^{2} + y^{2} + x y))

z (2 x + y)

Solution steps

\frac{\partial}{\partial x} ((z) (x^{2} + y^{2} + x y))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (x^{2} + y^{2} + x y)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= z (\frac{\partial}{\partial x} (x^{2}) + \frac{\partial}{\partial x} (y^{2}) + \frac{\partial}{\partial x} (x y))

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

\frac{\partial}{\partial x} (y^{2}) = 0

\frac{\partial}{\partial x} (x y) = y

= z (2 x + 0 + y)

Simplify

= z (2 x + y)

\frac{( 1 + a ) ^{n} + 2}{( 1 + a ) ^{2 n}}

\frac{2 x + 11}{( x - 2 ) ( x + 3 )}

(w - \frac{3}{2}) (w + \frac{7}{2})

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

3 x l e f t (5 x^{2} - 2 x + 1)

What is (\partial)/(\partial x)((z)(x^2+y^2+xy)) ?
The answer to (\partial)/(\partial x)((z)(x^2+y^2+xy)) is z(2x+y)