Derivatives involving trigonometric functions Calculate dy&gt;dx for the following functions. y=excos⁡x

Step 1 We will use the product rule y=excos⁡x dydx=ddx(ex)cos⁡x+exddx(cos⁡x) dydx=(ex)cos⁡x+ex(−sin⁡x) dydx=ex(cos⁡x−sin⁡x) Step 2 Answer: dydx=ex(cos⁡x−sin⁡x)

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banganX

Answered question

2021-10-23

Derivatives involving trigonometric functions Calculate dy>dx for the following functions.

y = e^{x} \cos x

Answer & Explanation

BleabyinfibiaG

Skilled2021-10-24Added 118 answers

Step 1
We will use the product rule

y = e^{x} \cos x

\frac{d y}{d x} = \frac{d}{d x} (e^{x}) \cos x + e^{x} \frac{d}{d x} (\cos x)

\frac{d y}{d x} = (e^{x}) \cos x + e^{x} (- \sin x)

\frac{d y}{d x} = e^{x} (\cos x - \sin x)

Step 2
Answer:

\frac{d y}{d x} = e^{x} (\cos x - \sin x)

Jeffrey Jordon

Expert2022-08-15Added 2605 answers

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