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

The answer to (\partial)/(\partial x)(3x^2y^2+x/y) is 6y^2x+1/y

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

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

6 y^{2} x + \frac{1}{y}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 6 y^{2} x + \frac{1}{y}

y = sin (3 x + 2 y)

\int (5 - 3 x + x^{2}) d x

\frac{d}{d x} (\frac{1}{5 - x})

f (x) = e^{- 2 x}, (0, 1)

y^{^{''}} - 2 y^{^{'}} + 10 y = e^{- x}

What is (\partial)/(\partial x)(3x^2y^2+x/y) ?
The answer to (\partial)/(\partial x)(3x^2y^2+x/y) is 6y^2x+1/y