derivative of xln(x)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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ddx (xln(x))

Solution

ln(x)+1

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Solution steps

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ddx (xln(x))

Apply the Product Rule: (f·g)′=f ′·g+f·g′

f=x, g=ln(x)

=dxdx ln(x)+ddx (ln(x))x

dxdx =1

ddx (ln(x))=1x

=1· ln(x)+1x x

Simplify 1· ln(x)+1x x: ln(x)+1

=ln(x)+1

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