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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) ?

 Oct 21, 2019

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 #1
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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).

 Oct 21, 2019
 #1
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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

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