What is (\partial)/(\partial x)((z)(4x^2+3y^2+3x)) ?

The answer to (\partial)/(\partial x)((z)(4x^2+3y^2+3x)) is z(8x+3)

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(\partial)/(\partial x)((z)(4x^2+3y^2+3x))

\frac{\partial}{\partial x} ((z) (4 x^{2} + 3 y^{2} + 3 x))

z (8 x + 3)

Solution steps

\frac{\partial}{\partial x} ((z) (4 x^{2} + 3 y^{2} + 3 x))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (4 x^{2} + 3 y^{2} + 3 x)

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (4 x^{2}) + \frac{\partial}{\partial x} (3 y^{2}) + \frac{\partial}{\partial x} (3 x))

\frac{\partial}{\partial x} (4 x^{2}) = 8 x

\frac{\partial}{\partial x} (3 y^{2}) = 0

\frac{\partial}{\partial x} (3 x) = 3

= z (8 x + 0 + 3)

Simplify

= z (8 x + 3)

(z - \frac{5}{3}) (z - \frac{2}{3})

(- 3 + i)^{10}

3 (2 - 510)

\frac{( x - 4 ) ( x - 1 ) ( x + 3 )}{( x - 3 ) ( x + 2 )}

(e - 1)^{2}

What is (\partial)/(\partial x)((z)(4x^2+3y^2+3x)) ?
The answer to (\partial)/(\partial x)((z)(4x^2+3y^2+3x)) is z(8x+3)