What is the derivative of x^3*y ?

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = y

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

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

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

\frac{d}{d x} ((9 x^{2} + x) (x - x^{2}))

\int \frac{x - 1}{e ^{x}} d x

\int \frac{2 x}{x ^{2} - 3} d x

\frac{1}{2 s ^{2} + 2 s + 1}

arctan (x^{\frac{1}{2}})

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