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aspifsGak5u

Answered question

2021-12-10

Calculating derivatives Find the derivative of the following functions.

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

Answer & Explanation

Durst37

Beginner2021-12-11Added 37 answers

Step 1
Consider the given function,

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

use the product rule of the differentiation which states that,

\frac{d}{d x} (u \cdot v) = u \frac{d v}{d x} + v \frac{d u}{d x}

Step 2
so differentiate the function considering

u = e^{x} and v = (\sin x + \cos x)

,

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

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

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

= 2 e^{x} \cos x

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