What is the derivative of 3x^3y-2x^2y^2+3y ?

The derivative of 3x^3y-2x^2y^2+3y is 3(3x^2y+(dy)/(dx)x^3)-2(2xy^2+2y(dy)/(dx)x^2)+3(dy)/(dx)

What is the first derivative of 3x^3y-2x^2y^2+3y ?

The first derivative of 3x^3y-2x^2y^2+3y is 3(3x^2y+(dy)/(dx)x^3)-2(2xy^2+2y(dy)/(dx)x^2)+3(dy)/(dx)

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\frac{d}{d x} (3 x^{3} y - 2 x^{2} y^{2} + 3 y)

3 (3 x^{2} y + \frac{d y}{d x} x^{3}) - 2 (2 x y^{2} + 2 y \frac{d y}{d x} x^{2}) + 3 \frac{d y}{d x}

Solution steps

\frac{d}{d x} (3 x^{3} y - 2 x^{2} y^{2} + 3 y)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (3 x^{3} y) - \frac{d}{d x} (2 x^{2} y^{2}) + \frac{d}{d x} (3 y)

\frac{d}{d x} (3 x^{3} y) = 3 (3 x^{2} y + \frac{d y}{d x} x^{3})

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

\frac{d}{d x} (3 y) = 3 \frac{d y}{d x}

= 3 (3 x^{2} y + \frac{d y}{d x} x^{3}) - 2 (2 x y^{2} + 2 y \frac{d y}{d x} x^{2}) + 3 \frac{d y}{d x}

What is the derivative of 3x^3y-2x^2y^2+3y ?
The derivative of 3x^3y-2x^2y^2+3y is 3(3x^2y+(dy)/(dx)x^3)-2(2xy^2+2y(dy)/(dx)x^2)+3(dy)/(dx)
What is the first derivative of 3x^3y-2x^2y^2+3y ?
The first derivative of 3x^3y-2x^2y^2+3y is 3(3x^2y+(dy)/(dx)x^3)-2(2xy^2+2y(dy)/(dx)x^2)+3(dy)/(dx)