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Popular >

derivative of-x^2y

Solution

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

Solution

- 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}

Popular Examples

derivative of sqrt(3-6x)derivative of

3 - 6 x

y^{''}-2y^'+y=6e^x

y^{^{''}} - 2 y^{^{'}} + y = 6 e^{x}

integral from 0 to 4 of 5x-x^2-x

\int_{0}^{4} 5 x - x^{2} - x d x

(\partial)/(\partial x)(ln(5+x^2y^2))

\frac{\partial}{\partial x} (ln (5 + x^{2} y^{2}))

integral of 3sqrt(x)+1/(sqrt(x))-1/x

\int 3 x + \frac{1}{x} - \frac{1}{x} d x

Frequently Asked Questions (FAQ)

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)