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

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

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

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

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

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

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

x^{2} + 2

y^{^{'}} + 3 y = 0, y (0) = 0

\frac{\partial}{\partial x} (e^{(y + 1) x})

f (x) = \frac{x ^{3} + 9 x ^{2} + x - 8}{x}

\frac{\partial}{\partial x} (4 a x)

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