What is the derivative of y=xlog_{e}(x) ?

The derivative of y=xlog_{e}(x) is ln(x)+1

What is the first derivative of y=xlog_{e}(x) ?

The first derivative of y=xlog_{e}(x) is ln(x)+1

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derivative of

y = x lo g_{e} (x)

ln (x) + 1

Solution steps

\frac{d}{d x} (x lo g_{e} (x))

Simplify

x lo g_{e} (x) : x ln (x)

= \frac{d}{d x} (x ln (x))

Apply the Product Rule:

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

f = x, g = ln (x)

= \frac{d x}{d x} ln (x) + \frac{d}{d x} (ln (x)) x

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= 1 \cdot ln (x) + \frac{1}{x} x

Simplify

1 \cdot ln (x) + \frac{1}{x} x : ln (x) + 1

= ln (x) + 1

What is the derivative of y=xlog_{e}(x) ?
The derivative of y=xlog_{e}(x) is ln(x)+1
What is the first derivative of y=xlog_{e}(x) ?
The first derivative of y=xlog_{e}(x) is ln(x)+1