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}

n \to \infty lim (\frac{n}{n})

n = 1 \sum \infty \frac{7}{n ^{2} + 36}

x \to 0 lim (∣ x ∣)

\int_{0}^{π} ∣ cos (x) ∣ d x

x \to 0 lim (- \frac{1}{1} + \frac{1}{x})

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