What is the integral or e^(-x)?
What is the derivative of - e-x ?
To find the integral of e^(-x), you can use the basic integration rule that states that the integral of e^(kx) dx equals (1/k) e^(kx) + C, where C is the constant of integration.
In this case, we have e^(-x), where k is -1. Applying the integration rule, the integral of e^(-x) dx is:
∫ e^(-x) dx = (1/-1) e^(-x) + C = -e^(-x) + C
So, the integral of e^(-x) is -e^(-x) + C.
Now, let's move on to finding the derivative of -e^(-x). The derivative of a function can be found using the power rule of differentiation, which states that the derivative of e^(kx) with respect to x is k * e^(kx).
In this case, we have -e^(-x), where k is -1. Applying the power rule, the derivative of -e^(-x) is:
d/dx (-e^(-x)) = -1 * e^(-x)
Therefore, the derivative of -e^(-x) is -e^(-x).