What is (\partial)/(\partial x)((y)(x^2+6xy+y^3)) ?

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

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(\partial)/(\partial x)((y)(x^2+6xy+y^3))

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

y (6 y + 2 x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (6 x y) = 6 y

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

= y (2 x + 6 y + 0)

Simplify

= y (6 y + 2 x)

(x + \frac{1}{4}) (x + \frac{3}{4})

j, m = 4 i - 7 j - k^{0}

k e^{8 (k + 1)}

(15 + j^{37.89}) x - (j^{37}, 89) y

\frac{1}{s e ^{3 (s - 1)}}

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