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

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

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

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

z (2 x + z y^{2})

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= z (2 x + z y^{2})

\frac{d}{d y} ((x) ((1 + 2 x)^{6}))

3 (1 - 2 sin^{2} (x) cos^{2} (x))

a (- 3, - 2) b (5, 3)

(x + 15 + x)^{2}

2 (2 x cos^{3} (x) - 3 x^{2} cos^{2} (x) sin (x))

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