What is the derivative of x-x^2y-y+xy^2 ?

The derivative of x-x^2y-y+xy^2 is 1-2xy-x^2(dy)/(dx)-(dy)/(dx)+y^2+2xy(dy)/(dx)

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

The first derivative of x-x^2y-y+xy^2 is 1-2xy-x^2(dy)/(dx)-(dy)/(dx)+y^2+2xy(dy)/(dx)

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

1 - 2 x y - x^{2} \frac{d y}{d x} - \frac{d y}{d x} + y^{2} + 2 x y \frac{d y}{d x}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

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

Simplify

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

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

What is the derivative of x-x^2y-y+xy^2 ?
The derivative of x-x^2y-y+xy^2 is 1-2xy-x^2(dy)/(dx)-(dy)/(dx)+y^2+2xy(dy)/(dx)
What is the first derivative of x-x^2y-y+xy^2 ?
The first derivative of x-x^2y-y+xy^2 is 1-2xy-x^2(dy)/(dx)-(dy)/(dx)+y^2+2xy(dy)/(dx)