**Problem : **
Compute the derivative of

g(x) = |

Applying the quotient rule yields

g'(x) | = | ||

= | |||

= |

**Problem : **
Find the derivative of

h(x) = e^{x2+sin(x)} |

Let

h'(x) | = | f'(g(x))g'(x) | |

= | (e^{x2+sin(x)})(2x + cos(x)) |

**Problem : **
Find the derivative of *g*(*x*) = log(*x*), noting that *g* has inverse *f* (*x*) = *e*^{x} and using
implicit differentiation.

f'(g(x))g'(x) = 1 |

or

g'(x) = |

In our case, this implies

g'(x) = = |

Figure %: Plot of *g*(*x*) = log(*x*) and *g'*(*x*) =

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