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

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

\int \frac{1}{9 - 16 x ^{2}} d x

\frac{d}{d x} (3 x^{4} - 2 x^{3} + 1)

\int 5 csc^{2} (x) d x

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

\int e^{(\frac{x ^{2}}{2})} d x

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