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

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

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

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

- 4 x + y^{3}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = 2 x - y^{3}

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

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

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

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

Simplify

- (1 \cdot (2 x - y^{3}) + 2 x) : - 4 x + y^{3}

= - 4 x + y^{3}

\frac{d}{d x} (\frac{1}{x ^{\frac{1}{2}}})

\int \frac{( x ^{2} )}{81 - x ^{2}} d x

\frac{d}{d x} ((2 x^{3} + 1)^{2})

(2, 6), (6, 6)

\frac{d}{d x} (- 6 sin (x) - 3 x)

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