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

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

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

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

4 x^{3} + 4 x y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 4 x^{3} + 4 y x + 0

Simplify

= 4 x^{3} + 4 x y

\int 3 y + 7 d y

\frac{\partial}{\partial x} (x^{2} \cdot e^{x \cdot y})

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

sec^{4} (x)

\int \frac{3}{x ^{2} ( x + 1 )} d x

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