# HSC Higher Mathematics 1st Paper Note 9th Chapter Differentiation

HSC Higher Mathematics 1st Paper Note 9th Chapter Differentiation. In the first section of this chapter, we saw the definition of the derivative and we computed a couple of derivatives using the definition. As we saw in those examples there was a fair amount of work involved in computing the limits and the functions that we worked with were not terribly complicated. For more complex functions using the definition of the derivative would be an almost impossible task. Luckily for us, we won’t have to use the definition terribly often. We will have to use it on occasion, however, we have a large collection of formulas and properties that we can use to simplify our life considerably and will allow us to avoid using the definition whenever possible. We will introduce most of these formulas over the course of the next several sections. We will start in this section with some of the basic properties and formulas. We will give the properties and formulas in this section in both “prime” notation and “fraction” notation.

## HSC Higher Mathematics 1st Paper Note 9th Chapter Differentiation

Solution (a)

In this case, we have the sum and difference of four terms and so we will differentiate each of the terms using the first property from above and then put them back together with the proper sign. Also, for each term with a multiplicative constant remember that all we need to do is “factor” the constant out (using the second property) and then do the derivative. Notice that in the third term the exponent was a one and so upon subtracting 1 from the original exponent we get a new exponent of zero. Now recall that. Don’t forget to do any basic arithmetic that needs to be done such as any multiplication and/or division in the coefficients.

[Return to Problems] (b)

The point of this problem is to make sure that you deal with negative exponents correctly. Here is the derivative. Make sure that you correctly deal with the exponents in these cases, especially the negative exponents. It is an easy mistake to “go the other way” when subtracting one off from a negative exponent and get instead of the correct.

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