What is (\partial)/(\partial y)((z)(6x^5+4y^3+4y)) ?

The answer to (\partial)/(\partial y)((z)(6x^5+4y^3+4y)) is z(12y^2+4)

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(\partial)/(\partial y)((z)(6x^5+4y^3+4y))

\frac{\partial}{\partial y} ((z) (6 x^{5} + 4 y^{3} + 4 y))

z (12 y^{2} + 4)

Solution steps

\frac{\partial}{\partial y} ((z) (6 x^{5} + 4 y^{3} + 4 y))

Treat

z, x

as constants

Take the constant out:

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

= z \frac{\partial}{\partial y} (6 x^{5} + 4 y^{3} + 4 y)

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial y} (6 x^{5}) + \frac{\partial}{\partial y} (4 y^{3}) + \frac{\partial}{\partial y} (4 y))

\frac{\partial}{\partial y} (6 x^{5}) = 0

\frac{\partial}{\partial y} (4 y^{3}) = 12 y^{2}

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

= z (0 + 12 y^{2} + 4)

Simplify

= z (12 y^{2} + 4)

\frac{x ^{4}}{( 1 - x ) ^{3}}

(3 x + 2 y - 2) d x + (6 x + 4 y + 4) d y

ln (\frac{x ^{3}}{y ^{2}})

- 5 (4 + 2)

What is (\partial)/(\partial y)((z)(6x^5+4y^3+4y)) ?
The answer to (\partial)/(\partial y)((z)(6x^5+4y^3+4y)) is z(12y^2+4)