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the function y=e^x is its own derivative. Show that for every value of c, y=c(e^x) has the same property

 Apr 11, 2020
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You could use the product rule:  

assuming that f(x) = a(x)·b(x)

then               f'(x) = a(x)·b'(x) + b(x)·a'(x)

 

For the problem  f(x)  =  x·ex, let a(x) = c  and  b(x) = ex,   (which makes a'(x) = 0 and b'(x) = ex)

then                   f'(x) = c·ex + ex·0

so                      f'(x) = c·ex 

 Apr 11, 2020

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