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

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

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

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

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

Solution steps

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

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

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

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

\frac{\partial}{\partial x} (3 y^{2}) = 0

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

Simplify

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

\frac{d}{d x} (\frac{1}{3} π x^{2} 100 - x^{2})

\frac{( e ^{- 4 s} )}{s + 2}

\frac{d}{d x} ((4^{x})^{9})

\frac{\partial}{\partial y} (5 x^{\frac{4}{5}} y^{\frac{1}{5}})

\int cos^{2} (t) + sin^{2} (t) d t

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