What is (\partial)/(\partial x)(2x^3y+8y^3) ?

The answer to (\partial)/(\partial x)(2x^3y+8y^3) is 6x^2y

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(\partial)/(\partial x)(2x^3y+8y^3)

\frac{\partial}{\partial x} (2 x^{3} y + 8 y^{3})

6 x^{2} y

Solution steps

\frac{\partial}{\partial x} (2 x^{3} y + 8 y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (2 x^{3} y) + \frac{\partial}{\partial x} (8 y^{3})

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

\frac{\partial}{\partial x} (8 y^{3}) = 0

= 6 y x^{2} + 0

Simplify

= 6 x^{2} y

\int 4 - x^{2} d x

\int \frac{1}{t t} d t

\int \frac{x}{( x ^{2} - 6 x + 10 ) ^{2}} d x

\frac{d}{d x} (e^{- 2 i x})

\frac{\partial}{\partial x} (\frac{6 x}{( x ^{2} + 9 )})

What is (\partial)/(\partial x)(2x^3y+8y^3) ?
The answer to (\partial)/(\partial x)(2x^3y+8y^3) is 6x^2y