What is the derivative of (xf(x))/5 ?

The derivative of (xf(x))/5 is (2xf)/5

What is the first derivative of (xf(x))/5 ?

The first derivative of (xf(x))/5 is (2xf)/5

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derivative

\frac{2 x f}{5}

Solution steps

\frac{d}{d x} (\frac{x f x}{5})

Treat

f

as a constant

Take the constant out:

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

= \frac{f}{5} \frac{d}{d x} (xx)

Apply the Product Rule:

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

f = x, g = x

= \frac{f}{5} (\frac{d x}{d x} x + \frac{d x}{d x} x)

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

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

= \frac{f}{5} (1 \cdot x + 1 \cdot x)

Simplify

\frac{f}{5} (1 \cdot x + 1 \cdot x) : \frac{2 x f}{5}

= \frac{2 x f}{5}

What is the derivative of (xf(x))/5 ?
The derivative of (xf(x))/5 is (2xf)/5
What is the first derivative of (xf(x))/5 ?
The first derivative of (xf(x))/5 is (2xf)/5