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

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

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

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

2 x y

Solution steps

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

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

\frac{\partial}{\partial x} (3 y^{2}) = 0

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

= 2 y x + 0 - 0

Simplify

= 2 x y

(\frac{e ^{4 x^{2}}}{x ^{2}})^{^{'}}

\int \frac{( 7 x ^{9} - 20 x ^{6} )}{x ^{3}} d x

\int (tan (x) + \frac{1}{tan ( x )})^{2} d x

x^{2} y^{^{''}} - 2 y = sin (ln (x))

x \to - 2 lim (2 x)

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