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

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

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

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

3 x^{2} + 2 x y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

\frac{\partial}{\partial x} (4 y^{3}) = 0

= 3 x^{2} + 2 y x - 0

Simplify

= 3 x^{2} + 2 x y

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

\int 7 tan^{3} (x) sec (x) d x

\frac{\partial}{\partial y} (1 + x^{3} + y^{4})

\frac{d x}{d t} = 0.25 - \frac{1}{20} x, x (0) = 0.5

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