What is (\partial)/(\partial x)(x^2+y^2(1-x)^3) ?

The answer to (\partial)/(\partial x)(x^2+y^2(1-x)^3) is 2x-3y^2(1-x)^2

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(\partial)/(\partial x)(x^2+y^2(1-x)^3)

\frac{\partial}{\partial x} (x^{2} + y^{2} (1 - x)^{3})

2 x - 3 y^{2} (1 - x)^{2}

Solution steps

\frac{\partial}{\partial x} (x^{2} + y^{2} (1 - x)^{3})

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} (y^{2} (1 - x)^{3})

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

\frac{\partial}{\partial x} (y^{2} (1 - x)^{3}) = - 3 y^{2} (1 - x)^{2}

= 2 x - 3 y^{2} (1 - x)^{2}

\frac{\partial}{\partial x} (\frac{x}{1 - x})

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What is (\partial)/(\partial x)(x^2+y^2(1-x)^3) ?
The answer to (\partial)/(\partial x)(x^2+y^2(1-x)^3) is 2x-3y^2(1-x)^2