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

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

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

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

3 x^{2} - 3 y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

= 3 x^{2} - 3 y^{2}

x \to 0 lim (\frac{e ^{2 x - 1}}{tan ( x )})

4 e^{2 t}

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

\frac{4 - x e ^{x}}{x + e ^{x}}

\frac{d y}{d t} = \frac{1}{t} y + 3 t

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