What is the derivative of (xy/2) ?

The derivative of (xy/2) is 1/2 (y+x(dy)/(dx))

What is the first derivative of (xy/2) ?

The first derivative of (xy/2) is 1/2 (y+x(dy)/(dx))

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

\frac{1}{2} (y + x \frac{d y}{d x})

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \frac{d}{d x} (x y)

Apply the Product Rule:

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

f = x, g = y

= \frac{1}{2} (\frac{d x}{d x} y + \frac{d y}{d x} x)

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

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

Simplify

= \frac{1}{2} (y + x \frac{d y}{d x})

What is the derivative of (xy/2) ?
The derivative of (xy/2) is 1/2 (y+x(dy)/(dx))
What is the first derivative of (xy/2) ?
The first derivative of (xy/2) is 1/2 (y+x(dy)/(dx))