What is the derivative of 4x-x^2y+y^3 ?

The derivative of 4x-x^2y+y^3 is 4-2xy-x^2(dy)/(dx)+3y^2(dy)/(dx)

What is the first derivative of 4x-x^2y+y^3 ?

The first derivative of 4x-x^2y+y^3 is 4-2xy-x^2(dy)/(dx)+3y^2(dy)/(dx)

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\frac{d}{d x} (4 x - x^{2} y + y^{3})

4 - 2 x y - x^{2} \frac{d y}{d x} + 3 y^{2} \frac{d y}{d x}

Solution steps

\frac{d}{d x} (4 x - x^{2} y + y^{3})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (4 x) - \frac{d}{d x} (x^{2} y) + \frac{d}{d x} (y^{3})

\frac{d}{d x} (4 x) = 4

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

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

= 4 - (2 x y + \frac{d y}{d x} x^{2}) + 3 y^{2} \frac{d y}{d x}

Simplify

4 - (2 x y + \frac{d y}{d x} x^{2}) + 3 y^{2} \frac{d y}{d x} : 4 - 2 x y - x^{2} \frac{d y}{d x} + 3 y^{2} \frac{d y}{d x}

= 4 - 2 x y - x^{2} \frac{d y}{d x} + 3 y^{2} \frac{d y}{d x}

\frac{s + 3}{s ^{2} + 4 s + 5}

\int \frac{11}{2 x 4 x ^{2} - 16} d x

\int \frac{( a x + b )}{( c x + d )} d x

\frac{7}{2 x ^{2}}

x \to \infty lim (arctan (x^{6} - x^{9}))

What is the derivative of 4x-x^2y+y^3 ?
The derivative of 4x-x^2y+y^3 is 4-2xy-x^2(dy)/(dx)+3y^2(dy)/(dx)
What is the first derivative of 4x-x^2y+y^3 ?
The first derivative of 4x-x^2y+y^3 is 4-2xy-x^2(dy)/(dx)+3y^2(dy)/(dx)