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

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

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(\partial)/(\partial x)(x^2(y-x))

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

2 x y - 3 x^{2}

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = y - x

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

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

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

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

Simplify

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

= 2 x y - 3 x^{2}

9 x y

\frac{d}{d x} (\frac{x + y + 1}{x - 1})

\int_{0}^{2 - y} \frac{5}{8} x^{3} d x

\frac{d}{d x} (cos (2 x) sin (\frac{x}{3}))

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

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