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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

(0, - 2), (2, 2)

\int_{0}^{1} x + 16 d x

sin (x + π)

2 e^{- 4 t}

\frac{d}{d x} (ln (\frac{y}{x}))

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