The derivative the a duty tells you the steep or price of readjust of the function. It"s a huge deal. Here are a few of the methods that the TI-89 deserve to calculate derivatives because that you.

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## The Derivative together a role

Sometimes girlfriend are provided a role and require to find the derivative that this function. Because that this, you have to use the TI-89"s "d) differentiate" function.

You can accessibility the differentiation duty from the Calc menu or indigenous . | |

The syntax that the duty is "d(function, variable)." for example, if y = x3 - 2x + 4, the derivative of y through respect to x can be found as in the screen shot at right. | |

The equipment to the difficulty "If x = 4t2 +1/t, uncover the derivative of x through respect come t" is shown at right. |

## Derivative in ~ a Point

Sometimes you just need to know the worth of the derivative that a role (the slope of the function"s graph) in ~ a specific point. There room a few ways to acquire this done. Suppose, for instance, the you want to recognize the steep of the graph the y = 0.4x2 + 1 in ~ the point where x = 3. Here are part methods:

You could use the "d) differentiate" duty along with the "|" operator. A feasible advantage of this method is that this function will shot to return specific value if possible. | |

If girlfriend graph the function, you deserve to use "6: Derivatives" indigenous the mathematics menu. Select "1: dy/dx" indigenous the submenu, and also then show the desired allude either by keying it and also pressing , or utilizing the blue arrowhead keys to relocate the cursor and then push . | |

The an outcome of making use of "6: Derivatives is shown at right. Be aware that the result of this role is always a decimal approximation. See more: Butcher And The Boar - Butcher & The Boar Restaurant | |

Alternatively, if friend graph the duty you have the right to use "A: Tangent" from the math menu. Choose the desired allude either by inputting it and pressing , or utilizing the blue arrowhead keys to move the cursor and then push . | |

The result of using "A: Tangent" is shown at right. Notice that this role draws the tangent line and also gives that (approximate) equation. |