What is (\partial)/(\partial x)(3x^4+5y^4+9xy) ?

The answer to (\partial)/(\partial x)(3x^4+5y^4+9xy) is 12x^3+9y

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(\partial)/(\partial x)(3x^4+5y^4+9xy)

\frac{\partial}{\partial x} (3 x^{4} + 5 y^{4} + 9 x y)

12 x^{3} + 9 y

Solution steps

\frac{\partial}{\partial x} (3 x^{4} + 5 y^{4} + 9 x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 x^{4}) + \frac{\partial}{\partial x} (5 y^{4}) + \frac{\partial}{\partial x} (9 x y)

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

\frac{\partial}{\partial x} (5 y^{4}) = 0

\frac{\partial}{\partial x} (9 x y) = 9 y

= 12 x^{3} + 0 + 9 y

Simplify

= 12 x^{3} + 9 y

What is (\partial)/(\partial x)(3x^4+5y^4+9xy) ?
The answer to (\partial)/(\partial x)(3x^4+5y^4+9xy) is 12x^3+9y