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Problems for "Derivatives of e x and of the Natural Log"

Problems for "Derivatives of e x and of the Natural Log"

Problems for "Derivatives of e x and of the Natural Log"

Problems for "Derivatives of e x and of the Natural Log"

Problems for "Derivatives of e x and of the Natural Log"

Problems for "Derivatives of e x and of the Natural Log"

Problem :

ex2 = ?    

ex2(2x)

Problem :

Πx = ?    

Πxln(Π)

Problem :

dx = ?    

3 lnx + c

Problem : 4xdx = ?

4x + c    

Problem :

x+5 = ?    

Must use logarithmic differentiation

y = x+5    

Take natural log of both sides and bring down exponents

ln y = 2x lnx+5    

Now differentiate, and remember to use the chain rule


 = 2x + ln(x + 5)(2)  
 = +2 ln(x+5)x+52x