Sometimes the inverse trig functions are notated with "arc" in front of their names rather than the superscript "-1". The table below shows both names for each function. sin−1x=arcsinxtan−1x=arctanxsec−1x=arcsecxcos−1x=arccosxcot−1x=arccotxcsc−1x=arccscxsin−1...
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By mastering these basic derivative rules, you’ll be well-equipped to differentiate a wide range of functions on the TI-89 calculator. In the next section, we’ll explore how to use the calculator’s derivative function to find derivatives more efficiently. So, let’s continue our derivative...
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Now, let's look at the parts still left to differentiate, beginning with: (xcos(x)+x)′ For the first term, we will need to use the product rule: ddx(xcos(x))=x(−sin(x))+1(cos(x))=cos(x)−xsin(x) And for the second term, we need the power ...
Note:There is no reason to expand the denominator. In fact, doing so will make the derivative harder to work with. Example 2 Supposef(x)=x2+64x+3f(x)=x2+64x+3. Findf′(x)f′(x). Step 1 Differentiate using the quotient rule. The parts inblueblueare related to the numerator. ...