Question

What is the derivative of ex?

Answer 1

Answer:

Step-by-step explanation:

(e^x)' = e^x

the derivative of e^x is e^x.

Answer 2

Proof of (d-dx) e^x : by (d-dx) ln(x)

Proof of (d-dx) e^x : by (d-dx) ln(x)Given : (d-dx) ln(x) = 1/x; Chain Rule; d/dx x = 1.

Proof of (d-dx) e^x : by (d-dx) ln(x)Given : (d-dx) ln(x) = 1/x; Chain Rule; d/dx x = 1.

Solve:

Proof of (d-dx) e^x : by (d-dx)

ln(x)Given : (d-dx) ln(x) = 1/x; Chain Rule; d/dx x = 1.Solve:(1) (d-dx) ln(e^x) = (d-dx) x = 1(d-dx) ln(e^x) = (d/du) ln(u) (d-dx) e^x (Set u=e^x)= 1/u (d-dx) e^x = 1/e^x (d-dx) e^x = 1 (equation 1)(d-dx) e^x = e^x

Hope it helps you