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)

Step-by-step differentiation using the Product Rule: The product rule states: If y = u · v, then
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) – e^x·sin(x) Final Answer is eˣ (cos(x) – sin(x))