Question

e^x কে ডেরিভেটিভ করলে কেন e^x ই হয়?

Answer 1

The differentiation of e to the power x is equal to e to the power x because the derivative of an exponential function with base 'e' is equal to e^x. Mathematically, it is denoted as d(ex)/dx = ex. e to the power x is an exponential function with a base equal to 'e'.

 

Suppose y = ex ⇒ ln y = ln ex ⇒ ln y = x. On differentiating this with respect to x, we have (1/y) dy/dx = 1 ⇒ dy/dx = y ⇒ dy/dx = ex

Answer 2

e^x =slope

And a derivative is an operater which obtains the slope (rate of change) .

So, derivative of e^x = the slope of a sloping surface . And the answer is e^x .

Therefore , derivative of e^x = e^x.