derivative of e^xcos(x)

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

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ddx

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

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ddx (e^xcos(x))

Solution

e^xcos(x)−e^xsin(x)

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ddx (e^xcos(x))

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

f=e^x, g=cos(x)

=ddx (e^x)cos(x)+ddx (cos(x))e^x

ddx (e^x)=e^x

ddx (cos(x))=−sin(x)

=e^xcos(x)+(−sin(x))e^x

Simplify

=e^xcos(x)−e^xsin(x)

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derivative of e^xcos(x)

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