What is (\partial)/(\partial x)((y)(x^3y^3-x^3+1)) ?

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

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(\partial)/(\partial x)((y)(x^3y^3-x^3+1))

\frac{\partial}{\partial x} ((y) (x^{3} y^{3} - x^{3} + 1))

y (3 y^{3} x^{2} - 3 x^{2})

Solution steps

\frac{\partial}{\partial x} ((y) (x^{3} y^{3} - x^{3} + 1))

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial x} (x^{3} y^{3} - x^{3} + 1)

Apply the Sum/Difference Rule:

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

= y (\frac{\partial}{\partial x} (x^{3} y^{3}) - \frac{\partial}{\partial x} (x^{3}) + \frac{\partial}{\partial x} (1))

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

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

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

= y (3 y^{3} x^{2} - 3 x^{2} + 0)

Simplify

= y (3 y^{3} x^{2} - 3 x^{2})

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\frac{100}{( j w + 5 ) ^{3}}

\frac{1}{( ( x - r ) ^{2} + y ^{2} + z ^{2} ) ^{\frac{5}{2}}}

\frac{1}{9 + 6 x}

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