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

The answer to (\partial)/(\partial x)(x^3+axy^2) is 3x^2+ay^2

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

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

3 x^{2} + a y^{2}

Solution steps

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

Treat

a, 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} (a x y^{2})

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

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

= 3 x^{2} + a y^{2}

x \to - \infty lim (\frac{4 arctan ( 8 x )}{e ^{x} + 2})

\int x d x

\frac{\partial}{\partial y} (6 y^{5} cos (5 x))

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

\int 3 y + 7 d y

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