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

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

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

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

z (2 x + y)

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= z (2 x + y + 0)

Simplify

= z (2 x + y)

\frac{( 6 x - 5 ) ( x - 6 )}{x - 5}

\frac{( 2 + x ) ( 3 + 2 x ) ^{2}}{( 1.8 - 2 x ) ^{2} ( 1 - 2 x ) ^{2}}

x (4 - x + 2)

\frac{( k ( k + 1 ) ( k + 2 ) )}{3}

\frac{s - 1}{( s - 2 ) ( s - 3 )}

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