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Log and Exponential Differentiation Exercises

Exercises from public domain textbooks. Solutions where provided do not necessary follow the same lines as the original.

Solutions are not given for exercises whose number is not linked

Some workings are given for exercises which do not have a textbook solution. These may contain errors.

Calculate the derivative of each of the following functions. When possible, simplify the given expression first.

C65-1. {$$ \log_{10} x^3 $$}

worked

C65-2. {$$ \log_{10} \sqrt{x} $$}

worked

C65-3. {$$ \log_{10} (1+2x) $$}

worked

C65-4. {$$ \log_{10} (1+x^3) $$}

worked

C65-5. {$$ \log_e (1+x)^3 $$}

worked

C65-6. {$$ \log_e \sqrt{3+5x} $$}

worked

C65-7. {$$ \log_e ({1 \over x})$$}

worked

C65-8. {$$ \log_{10} (x^{-3}) $$}

worked

C65-9. {$$ x \log_e x^2 $$}

worked

C65-10. {$$ \log_e \left( {{1-x} \over {1+x}} \right) $$}

worked

C65-11. {$$ \log_{10} \left( 2 - {t \over {1-t}} \right) $$}

Warning! Textbook answer does not agree in sign with worked answer (and textbook answer is geometrically implausible).

worked

C65-12. {$$ \log_e {t \over {\sqrt{1-t^2}}}$$}

worked

C65-13. {$$ {{\log_e t} \over t} $$}

worked

C65-14. {$$ \log_e \{log_e x \} $$}

worked

C65-15. {$$ (\log_e t)^4 $$}

Warning! Textbook answer does not agree with worked answer.

worked

C67-1. {$$ e^{3x} $$}

worked

C67-2. {$$ e^{2x+x^2} $$}

worked

C67-3. {$$ e^{\sqrt{1+x}} $$}

worked

C67-4. {$$ e^{\log x} $$}

worked

C67-5. {$$ x^2e^x $$}

worked

C67-6. {$$ (1-x)^3e^{x^2} $$}

worked

C67-7. {$$ 10^{3x+4} $$}

worked

C67-8. {$$ a^{(1+x)^3} $$}

worked

C67-9. {$$ \log e^x $$}

worked

C67-10. {$$ \log (1+e^x) $$}

worked

C67-11. {$$ \log e^{-x^2} $$}

worked

C67-12. {$$ (\log e^{2x})^2 $$}

worked

C67-13. {$$ (e^x + 1)^2 $$}

worked

C67-14. {$$ {{e^{\sqrt{x}} + e^{-\sqrt{x}} } \over 2} $$}

worked

C67-15. {$$ {{e^{\sqrt{x}} - e^{-\sqrt{x}} } \over 2} $$}

worked

C67-16. {$$ {{e^x - e^{-x}} \over {e^x + e^{-x}}} $$}

worked

C67-17. Show that the slope of the curve {$ y=e^x $} is equal to its ordinate.


Sources:

Recommended:

Category: Math Calculus


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This is a student's notebook. I am not responsible if you copy it for homework, and it turns out to be wrong.

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August 05, 2017

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