What is (\partial)/(\partial x)(6x^3y+6y^5+1) ?

The answer to (\partial)/(\partial x)(6x^3y+6y^5+1) is 18x^2y

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(\partial)/(\partial x)(6x^3y+6y^5+1)

\frac{\partial}{\partial x} (6 x^{3} y + 6 y^{5} + 1)

18 x^{2} y

Solution steps

\frac{\partial}{\partial x} (6 x^{3} y + 6 y^{5} + 1)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (6 x^{3} y) + \frac{\partial}{\partial x} (6 y^{5}) + \frac{\partial}{\partial x} (1)

\frac{\partial}{\partial x} (6 x^{3} y) = 18 y x^{2}

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

\frac{\partial}{\partial x} (1) = 0

= 18 y x^{2} + 0 + 0

Simplify

= 18 x^{2} y

What is (\partial)/(\partial x)(6x^3y+6y^5+1) ?
The answer to (\partial)/(\partial x)(6x^3y+6y^5+1) is 18x^2y