What is (\partial)/(\partial x)((z)(3x^2+6y^2+4)) ?

The answer to (\partial)/(\partial x)((z)(3x^2+6y^2+4)) is 6zx

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(\partial)/(\partial x)((z)(3x^2+6y^2+4))

\frac{\partial}{\partial x} ((z) (3 x^{2} + 6 y^{2} + 4))

6 z x

Solution steps

\frac{\partial}{\partial x} ((z) (3 x^{2} + 6 y^{2} + 4))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (3 x^{2} + 6 y^{2} + 4)

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (3 x^{2}) + \frac{\partial}{\partial x} (6 y^{2}) + \frac{\partial}{\partial x} (4))

\frac{\partial}{\partial x} (3 x^{2}) = 6 x

\frac{\partial}{\partial x} (6 y^{2}) = 0

\frac{\partial}{\partial x} (4) = 0

= z (6 x + 0 + 0)

Simplify

= 6 z x

\frac{3 ab}{( a + b ) ^{3}}

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

\frac{4 s + 5}{( s + 3 ) ^{2}}

(2 x y + 3) d x

\frac{5}{x ( x + 5 )}

What is (\partial)/(\partial x)((z)(3x^2+6y^2+4)) ?
The answer to (\partial)/(\partial x)((z)(3x^2+6y^2+4)) is 6zx