What is (\partial)/(\partial x)((z)(z^x-4xy^3+z)) ?

The answer to (\partial)/(\partial x)((z)(z^x-4xy^3+z)) is z(z^xln(z)-4y^3)

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(\partial)/(\partial x)((z)(z^x-4xy^3+z))

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

z (z^{x} ln (z) - 4 y^{3})

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (z^{x}) = z^{x} ln (z)

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

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

= z (z^{x} ln (z) - 4 y^{3} + 0)

Simplify

= z (z^{x} ln (z) - 4 y^{3})

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

(\frac{1}{2}, \frac{7}{2}) y (- \frac{8}{5}, - \frac{6}{5})

- \frac{( 4 - 3 π ) a ^{3}}{18}

(e^{10} - 1)^{2}

8 + (8 - cos (4 t)) U (t - 2 π)

What is (\partial)/(\partial x)((z)(z^x-4xy^3+z)) ?
The answer to (\partial)/(\partial x)((z)(z^x-4xy^3+z)) is z(z^xln(z)-4y^3)