What is the derivative of f(x)=e^-3x
What is -3*e^-3x ? You ought to have this in your head, automatically.
f=e^ax
f'= a*e^ax
f"=a^2*e^ax
Thats what I thought but the negative threw me off. I didn't know if I needed to subtract 1 to remove the negative. Or if that mattered in this equation.
To find the derivative of the function f(x) = e^-3x, you can use the chain rule. The chain rule states that if you have a function of the form g(h(x)), then its derivative can be found by multiplying the derivative of g with the derivative of h.
In this case, let's take g(u) = e^u and h(x) = -3x. The derivative of g(u) with respect to u is simply e^u. The derivative of h(x) with respect to x is -3.
Now, we can apply the chain rule. The derivative of f(x) = e^-3x is:
f'(x) = g'(h(x)) * h'(x)
= e^(-3x) * -3
= -3e^(-3x)
So, the derivative of f(x) = e^-3x is -3e^(-3x).