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

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

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

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

2 y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (2 x y) = 2 y

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

= 2 y + 0

Simplify

= 2 y

\int_{0}^{1} \frac{1}{t + 1} d t

\frac{d y}{d x}, x y = 36

\frac{d y}{d t} + 2 t y = 2 t

\int \frac{1}{x ^{2} ( e ^{\frac{1}{x}} - 5 )} d x

\int \frac{1}{2} x^{2} - 2 x + 6 d x

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