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

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

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

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

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

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

Solution steps

\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}

= \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}

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

x \to 0 lim (x sin (\frac{7 π}{x}))

\frac{x ln ( x + e )}{x ^{3} + e ^{x}}

2 x^{2} - 3 x + 6, at x = 2

n = 5 \sum \infty n! (x - 4)^{n}

x^{2}

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