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Problems for "Derivatives of ex and of the Natural Log"

Problems for "Derivatives of ex and of the Natural Log"

Problems for "Derivatives of ex and of the Natural Log"

Problems for "Derivatives of ex and of the Natural Log"

Problems for "Derivatives of ex and of the Natural Log"

Problems for "Derivatives of ex and of the Natural Log"

Problem :

e x2 = ?    

e x2 (2x)

Problem :

Π x = ?    

Π xln(Π)

Problem :

dx = ?    

3 ln x + c

Problem : 4x dx = ?

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 ln x+5    

Now differentiate, and remember to use the chain rule


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