What is (\partial)/(\partial x)((y)(3x^2-12y)) ?

The answer to (\partial)/(\partial x)((y)(3x^2-12y)) is 6yx

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(\partial)/(\partial x)((y)(3x^2-12y))

\frac{\partial}{\partial x} ((y) (3 x^{2} - 12 y))

6 y x

Solution steps

\frac{\partial}{\partial x} ((y) (3 x^{2} - 12 y))

Treat

y

as a constant

Take the constant out:

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

= y \frac{\partial}{\partial x} (3 x^{2} - 12 y)

Apply the Sum/Difference Rule:

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

= y (\frac{\partial}{\partial x} (3 x^{2}) - \frac{\partial}{\partial x} (12 y))

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

\frac{\partial}{\partial x} (12 y) = 0

= y (6 x - 0)

Simplify

= 6 y x

\frac{12}{( x + 12 ) ^{2}}

\frac{d ^{2}}{d x ^{2}} ((y) (- 4 x + 40))

x y^{''} (x) + 2 y^{'} (x) - \frac{2 x y}{( 1 - x ) ^{2}}

\frac{( ( s + 1 ) ^{3} )}{s ^{4}}

\frac{2 + s ^{2}}{s ( s ^{2} + 1 )}

What is (\partial)/(\partial x)((y)(3x^2-12y)) ?
The answer to (\partial)/(\partial x)((y)(3x^2-12y)) is 6yx