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

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

= 4 x - y^{3}

y = 5 x + 6, (2, 4)

\int (x + 3)^{2} sin (x) d x

\frac{d}{d x} (sin (- 4 x))

(x^{2} + 1) \frac{d y}{d x} + 4 x y = x

\frac{( x )}{x + 1}

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