What is the derivative of x*y^2 ?

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = y^{2}

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

\frac{d x}{d x} = 1

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

= 1 \cdot y^{2} + 2 y \frac{d y}{d x} x

Simplify

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

t^{\frac{5}{2}}

\int x^{4} e^{(x^{5})} d x

x \to 5 lim (\frac{x ^{2} + 1}{x - 5})

\frac{1}{s ^{2} - 2 s + 3}

\frac{\partial}{\partial x} (3 x^{2} - 2 x + 6 y^{2} + 2 y + 2)

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