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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

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

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

Simplify

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

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

x \to - 6 lim (\frac{x + 1 + 5}{x + 6})

x \to 9 lim (\frac{2 x - 1}{x + 3})

\frac{\partial}{\partial z} (x \cdot cos (y) \cdot sin (z))

\frac{d}{d t} (\frac{1}{t ^{2} + 1})

\frac{\partial}{\partial x} ((x + y^{2}) \cdot e^{3 x - 2 y})

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