What is the derivative of x^3y^3 ?

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

What is the first derivative of x^3y^3 ?

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

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

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

Solution steps

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{3}, g = y^{3}

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

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

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

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

\frac{\partial}{\partial x} (3 x e^{x y})

d er i v a t i v e x sin (y)

x \to - \infty lim (- 2 x - 1)

\int 25 - 4 x^{2} d x

t an g e n t y = 2 sin (x), at x = \frac{π}{4}

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