### Introduction to differentiation: Conclusion introduction to differentiation

### Summary

In this chapter you have become acquainted with the notion of derivative of a function and you have learned what the derivatives of several standard functions are. This is summarized in the table below.

function |
derivative |

#f(x)=c# (a constant) | #f'(x)=0# |

#f(x)=x^n#, where #n# is a natural number | #f'(x)=nx^{n-1}# |

#f(x)=x^a#, where #a# is a real number, for #x\gt0# | #f'(x)=ax^{a-1}# |

#f(x)=\exp(x)# | #f'(x)=\exp(x)# |

#f(x)=a^x#, where #a\gt0# | # f'(x)=a^x\cdot\ln(a)# |

#f(x)=\ln(x)#, for #x\gt0# | #f'(x)=\frac{1}{x}# |

#f(x)= \log_a(x)# | #f'(x)=\frac{1}{x \cdot \ln(a)}# |

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