Using the chain rule

Question

f(x)=e^ax cos(bx) for constants a and b

Answer 1

To find f'(x) use the product rule and the chain rule.

f'(x) = e^ax(-sin(bx))(b) + cos(bx)e^ax(a)

= e^ax(acos(bx) - bsin(bx)]

Here is a Desmos graph for confirmation along with a sliding point on f(x) that uses f'(x) to generate the equation of the tangent line at that sliding point.

desmos.com/calculator/axdt0f1ypa