Question

Find the derivative of
eˣ(cos(x)−sin(x)).

Answer 1

To find the derivative of eˣ(cos(x)−sin(x)), use the product rule and the chain rule.

Step-by-step explanation:

To find the derivative of eˣ(cos(x)−sin(x)), we can use the product rule and the chain rule. Let's start by differentiating the function term by term:

• The derivative of eˣ is eˣ.
• The derivative of cos(x)−sin(x) is -sin(x) - cos(x).

Now, using the product rule, we get:

(eˣ)(-sin(x) - cos(x)) + eˣ(0 - sin(x)) = -eˣsin(x) - eˣcos(x).