What is (\partial)/(\partial x)(-6x^3+10y^2-4xy) ?

The answer to (\partial)/(\partial x)(-6x^3+10y^2-4xy) is -18x^2-4y

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(\partial)/(\partial x)(-6x^3+10y^2-4xy)

\frac{\partial}{\partial x} (- 6 x^{3} + 10 y^{2} - 4 x y)

- 18 x^{2} - 4 y

Solution steps

\frac{\partial}{\partial x} (- 6 x^{3} + 10 y^{2} - 4 x y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= - \frac{\partial}{\partial x} (6 x^{3}) + \frac{\partial}{\partial x} (10 y^{2}) - \frac{\partial}{\partial x} (4 x y)

\frac{\partial}{\partial x} (6 x^{3}) = 18 x^{2}

\frac{\partial}{\partial x} (10 y^{2}) = 0

\frac{\partial}{\partial x} (4 x y) = 4 y

= - 18 x^{2} + 0 - 4 y

Simplify

= - 18 x^{2} - 4 y

\int (- 3 x + 4) e^{- x} d x

\frac{d y}{d x} = \frac{( 2 y + 1 )}{( x + 1 )}

x^{^{'}} x - 5 x = 25

f (x) = \frac{x}{x + 7}

y^{^{'''}} + y^{^{''}} = x - e^{- x}

What is (\partial)/(\partial x)(-6x^3+10y^2-4xy) ?
The answer to (\partial)/(\partial x)(-6x^3+10y^2-4xy) is -18x^2-4y