What is (\partial)/(\partial x)((z)(x^4-4xy+9y^3)) ?

The answer to (\partial)/(\partial x)((z)(x^4-4xy+9y^3)) is z(4x^3-4y)

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(\partial)/(\partial x)((z)(x^4-4xy+9y^3))

\frac{\partial}{\partial x} ((z) (x^{4} - 4 x y + 9 y^{3}))

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

Solution steps

\frac{\partial}{\partial x} ((z) (x^{4} - 4 x y + 9 y^{3}))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (x^{4} - 4 x y + 9 y^{3})

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (x^{4}) - \frac{\partial}{\partial x} (4 x y) + \frac{\partial}{\partial x} (9 y^{3}))

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

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

\frac{\partial}{\partial x} (9 y^{3}) = 0

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

Simplify

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

\frac{1}{( x + 1 ) \cdot ( x ^{3} - 1 )}

x (54 - 4 ln (x))

\frac{50 ( s - 2 )}{s ( s ^{2} + s + 100 )}

\frac{5}{s ( s ^{2} + 10 s + 8 )}

\frac{s + 1}{s ( s ^{2} + s + 1 )}

What is (\partial)/(\partial x)((z)(x^4-4xy+9y^3)) ?
The answer to (\partial)/(\partial x)((z)(x^4-4xy+9y^3)) is z(4x^3-4y)