Final answer:
To find the derivative of the expression 9x⋅13xeˣ, we can use the product rule. Applying the product rule, the derivative is 9eˣ + 13xeˣ + 117xeˣ.
Step-by-step explanation:
The given expression is 9x⋅13xeˣ. To find the derivative of this expression, we can use the product rule. The product rule states that if we have two functions, f(x) and g(x), then the derivative of their product is f'(x)g(x) + f(x)g'(x).
Applying the product rule to the given expression, we have:
(9x⋅13xeˣ)' = (9x)'⋅13xeˣ + 9x⋅(13xeˣ)'
The derivative of 9x with respect to x is 9, and the derivative of 13xeˣ with respect to x is 13eˣ + 13xeˣ. Therefore, the derivative of 9x⋅13xeˣ is 9(13xeˣ) + 9x(13eˣ + 13xeˣ), which simplifies to 9eˣ + 13xeˣ + 117xeˣ.