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# Differentiate. $f(x) = e^x$ cos $x$

## $$f^{\prime}(x)=e^{x}(-\sin x)+(\cos x) e^{x}=e^{x}(\cos x-\sin x)$$

Derivatives

Differentiation

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##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

Hey, it's clear. So when you read here So we're gonna get D of t x of E to the X Times co sign of sex. He's the product rule, so we get E to the X d over the ex of co sign nuts. Less co sign of x d Over the ex Both need to the ex. This becomes negative Sign acts. Ms becomes e to the X. So this is heat The X Times co sign That's minus sign the offense.

#### Topics

Derivatives

Differentiation

##### Catherine R.

Missouri State University

##### Heather Z.

Oregon State University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp