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

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

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

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

2 x + 3 y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= 2 x + 3 y^{2}

\frac{2 s - 7}{( s - 4 ) ( s + 6 )}

\int \frac{x + 4}{x ^{2} + 5 x - 6} d x

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

\int_{3}^{0} (5 x - x^{3}) d x

y^{^{'}} = \frac{3 y ^{2} + 3}{2 x y}

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