Hello, in my Math Class i was taught that d/dx(e^x) = e^x. This calculator is adding *ln(e) why would that be?

Also d/dax(e^(a*x)) = e^(a*x)*ln(e)** but **d/dx(e^(3*x))= 3e^(3x)*ln(e)

So shouldn´t d/dax(...) be a*e^(a*x)*ln(e) ?

Guest Oct 21, 2019

#1**0 **

ln(e) = 1 so it needn't be there, (shouldn't be there). It looks like it's a ' feature ' of your calculator.

In the middle line, the first derivative is wrt ax, the second simply wrt x, it isn't that you are simply replacing a by 3.

On the third line, study the effect of replacing ax by the variable y (=ax), ie. d/dy(e^(y) )= e^(y).

Guest Oct 21, 2019

#1**0 **

Best Answer

ln(e) = 1 so it needn't be there, (shouldn't be there). It looks like it's a ' feature ' of your calculator.

In the middle line, the first derivative is wrt ax, the second simply wrt x, it isn't that you are simply replacing a by 3.

On the third line, study the effect of replacing ax by the variable y (=ax), ie. d/dy(e^(y) )= e^(y).

Guest Oct 21, 2019