What is (\partial)/(\partial x)(3x+4y^2+3x^2y^3) ?

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

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(\partial)/(\partial x)(3x+4y^2+3x^2y^3)

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

6 x y^{3} + 3

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (4 y^{2}) = 0

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

= 3 + 0 + 6 y^{3} x

Simplify

= 6 x y^{3} + 3

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