What is the derivative of-x^2y ?

The derivative of-x^2y is -2xy-x^2(dy)/(dx)

What is the first derivative of-x^2y ?

The first derivative of-x^2y is -2xy-x^2(dy)/(dx)

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

- 2 x y - x^{2} \frac{d y}{d x}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

f = x^{2}, g = y

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

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

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

Simplify

- (2 x y + \frac{d y}{d x} x^{2}) : - 2 x y - x^{2} \frac{d y}{d x}

= - 2 x y - x^{2} \frac{d y}{d x}

What is the derivative of-x^2y ?
The derivative of-x^2y is -2xy-x^2(dy)/(dx)
What is the first derivative of-x^2y ?
The first derivative of-x^2y is -2xy-x^2(dy)/(dx)