What is (\partial)/(\partial x)((y)(x^3y-x-5y-10)) ?

The answer to (\partial)/(\partial x)((y)(x^3y-x-5y-10)) is y(3yx^2-1)

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(\partial)/(\partial x)((y)(x^3y-x-5y-10))

\frac{\partial}{\partial x} ((y) (x^{3} y - x - 5 y - 10))

y (3 y x^{2} - 1)

Solution steps

\frac{\partial}{\partial x} ((y) (x^{3} y - x - 5 y - 10))

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial x} (x^{3} y - x - 5 y - 10)

Apply the Sum/Difference Rule:

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

= y (\frac{\partial}{\partial x} (x^{3} y) - \frac{\partial}{\partial x} (x) - \frac{\partial}{\partial x} (5 y) - \frac{\partial}{\partial x} (10))

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

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

\frac{\partial}{\partial x} (5 y) = 0

\frac{\partial}{\partial x} (10) = 0

= y (3 y x^{2} - 1 - 0 - 0)

Simplify

= y (3 y x^{2} - 1)

(x^{2} - 5)^{8} \cdot 2 x d x

\frac{( 4 - 3 i ) ^{6}}{6}

(2 x^{3} + \frac{b}{x})^{8}

ln (z) (z - 1)^{8}

(cos (x) + sin (y))^{2}

What is (\partial)/(\partial x)((y)(x^3y-x-5y-10)) ?
The answer to (\partial)/(\partial x)((y)(x^3y-x-5y-10)) is y(3yx^2-1)