Question

antiderivative of e^-x

Answer 1

what is the derivative of e^-x

Answer 2

the derivative of e^-x is
-e^-x so wat wud you do to take it back to be e^-x

Answer 3

this is what though on doing e^-x=e/x

Answer 4

so the antiderivative is lnx=1/x times e

Answer 5

@Jonask, that does not suffice to answer the question. If F is the antiderivative of f, there is nothing to link F and f'. If anything, you'd have to integrate twice.

The antiderivative is -e^(-x). If you differentiate this, you get back e^-x by the chain rule. The way you could get this is by a u substitution of u = -x. du = -dx. Thus your integral becomes -e^u with respect to u. As you know, this integral is simply -e^u + c. Substituting back for u, you get the antiderivative to be -e^(-x) + c

@sermusart that is wrong. the derivative of ln(x) is 1/x. e^-x is NOT equal to 1/x. lnx is the inverse of of e^x and has nothing to do with this problem.