Question
The derivative of y = eˣ · cos(x) is
Solution
We have a function
y = eˣ · cos(x)
which is a product of two functions:
- First function: u = eˣ
- Second function: v = cos(x)
dy/dx = (du/dx)·v + u·(dv/dx) Now, differentiate each part: 1. u = eˣ ⇒ du/dx = eˣ 2. v = cos(x) ⇒ dv/dx = –sin(x) Now apply the product rule: dy/dx = (eˣ)·cos(x) + (eˣ)·(–sin(x))
= eˣ·cos(x) – ex·sin(x) Final Answer is eˣ (cos(x) – sin(x))
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