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

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

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

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

y (y^{2} + 6 x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

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

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

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

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

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

= y (6 x + y^{2} + 0)

Simplify

= y (y^{2} + 6 x)

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

e^{x (x - 3)}

\frac{6 x}{( 5 + 3 x ^{2} ) ^{4}}

\frac{1}{( x + 2 ) ( x - 3 )}

\frac{( x - 6 ) ^{2}}{x}

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