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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = y^{2}

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

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

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

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

y = \frac{x ^{3}}{3} - x^{2} - 3 x

f (x) = 5 + x + x^{2}

y = x^{2} + \frac{16}{x}

f (x) = 2 x^{3} - 3 x^{2} - 252 x

y = 2 x^{3} + a x^{2} - 12 x - 4, x = 1

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