derivative of cos(xsin(x))

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

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ddx (cos(x)sin(x))

Solution

cos(2x)

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ddx (cos(x)sin(x))

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

f=cos(x), g=sin(x)

=ddx (cos(x))sin(x)+ddx (sin(x))cos(x)

ddx (cos(x))=−sin(x)

ddx (sin(x))=cos(x)

=(−sin(x))sin(x)+cos(x)cos(x)

Simplify (−sin(x))sin(x)+cos(x)cos(x): cos(2x)

=cos(2x)

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

derivative of cos(xsin(x))

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