Find the derivative of the following function.𝑓(𝑥)=𝑒𝑥sin(𝑥)𝑓′(𝑥)=

To find the derivative of the function f(x) = e^x * sin(x), we will use the product rule. The product rule states that the derivative of the product of two functions is the derivative of the first times the second plus the first times the derivative of the second.

Let's denote: u(x) = e^x (the first function) v(x) = sin(x) (the second function)

We need to find the derivatives of these two functions: u'(x) = e^x (the derivative of e^x is e^x itself) v'(x) = cos(x) (the derivative of sin(x) is cos(x))

Now, we can apply the product rule: f'(x) = u'(x)v(x) + u(x)v'(x) f'(x) = e^x * sin(x) + e^x * cos(x)

So, the derivative of the function f(x) = e^x * sin(x) is f'(x) = e^x * sin(x) + e^x * cos(x).