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

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

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

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

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

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

Solution steps

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

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 y)

\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 y) = y + x \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}) + y + x \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}) + y + x \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} + y + x \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} + y + x \frac{d y}{d x}

2 x^{2} + \frac{1}{x ^{2}}

\int \frac{x ^{3}}{( x ^{2} - 256 ) ^{\frac{3}{2}}} d x

(0, - 10), (6, 10)

\frac{2}{5 x ^{3}}

f (x) = 1 - x - 2 x^{2}, at x = 2

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