Find the derivative of $f(t)=(25-t)\times e^{0.1t}$

Question

I've been trying to find the derivative of the function for quite a while but I just can't find it.

Can anybody please help me?

Answer 1

$f(t) = (25-t)e^{0.1t}$.

First understand that there are two functions: $(25 - t)$, and $(e^{0.1t})$. Thus we have to apply product rule, but notice that to differentiate $(e^{0.1t})$, we have a function in a function, so we must use chain rule here.

The derivative of $(25 - t)$ = $-1$.

The derivative of $(e^{0.1t}$) = $0.1e^{0.1t}.$

Doing the product rule, we have:

$$(h(x)g(x))' = h'(x)g(x) + h(x)g'(x)$$ $$((25-t)e^{0.1t})' = (-1)(e^{0.1t}) + (25 - t)(0.1e^{0.1t})$$