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

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

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

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

8 z x^{3}

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 x^{4}) = 8 x^{3}

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

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

= z (8 x^{3} + 0 + 0)

Simplify

= 8 z x^{3}

(2 x - \frac{1}{y})^{4}

\frac{64}{r ( - x + r )}

2 (3 + lo g_{10} (2))

(x y - 3) (x y + 3)

(3 x + 2 y) d x

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