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Popular >

derivative of-xy^2

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = y^{2}

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

\frac{d x}{d x} = 1

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

= - (1 \cdot y^{2} + 2 y \frac{d y}{d x} x)

Simplify

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

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

Popular Examples

inverse oflaplace 9/(s(s^2+9s+9))inverse laplace

\frac{9}{s ( s ^{2} + 9 s + 9 )}

tangent of f(x)=e^x+1,\at x=0 tangent of

f (x) = e^{x} + 1, at x = 0

tangent of f(x)= 4/(x^5)-1/(x^2),\at x=1 tangent of

f (x) = \frac{4}{x ^{5}} - \frac{1}{x ^{2}}, at x = 1

derivative of y=x^3-13x^2+48x+8 derivative of

y = x^{3} - 13 x^{2} + 48 x + 8

integral from 0 to 1 of (sqrt(x))^2

\int_{0}^{1} (x)^{2} d x

Frequently Asked Questions (FAQ)

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