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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Product Rule:

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

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

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

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

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

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

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