What is (\partial)/(\partial x)(x^2y+1/y) ?

The answer to (\partial)/(\partial x)(x^2y+1/y) is 2xy

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(\partial)/(\partial x)(x^2y+1/y)

\frac{\partial}{\partial x} (x^{2} y + \frac{1}{y})

2 x y

Solution steps

\frac{\partial}{\partial x} (x^{2} y + \frac{1}{y})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{2} y) + \frac{\partial}{\partial x} (\frac{1}{y})

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

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

= 2 y x + 0

Simplify

= 2 x y

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

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

5 \cdot i (t)

\frac{x ^{\frac{1}{3}} - 4}{x ^{\frac{7}{2}}}

y^{^{''}} + 10 y^{^{'}} + 25 y = - 50 e^{- 5 x}

What is (\partial)/(\partial x)(x^2y+1/y) ?
The answer to (\partial)/(\partial x)(x^2y+1/y) is 2xy