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[-/4 Points]DETAILSLARCALCTI 2.3.027.Complete the table to find the derivative of the function without using the Quotient Rule Function Rewrite Differentiate Simpl...

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[-/4 Points]DETAILSLARCALCTI 2.3.027.Complete the table to find the derivative of the function without using the Quotient Rule Function Rewrite Differentiate Simplify 9+3/2Need Help?RendltIkte QutelSubmit Answer

[-/4 Points] DETAILS LARCALCTI 2.3.027. Complete the table to find the derivative of the function without using the Quotient Rule Function Rewrite Differentiate Simplify 9+3/2 Need Help? Rendlt Ikte Qutel Submit Answer



Answers

Complete the table to find the derivative of the function without using the Quotient Rule. Function - Rewrite - Differentiate - Simplify $$y=\frac{4 x^{3 / 2}}{x}$$

Mhm For this problem we are asked to complete the table without using the quotient. Starting with the function Y equals four X. Four of 3/2 over X. So we're asked to rewrite this first Now four x power of 3/2 over X can be written as four times X power of 3/2 times X power of negative one. Which in turn can be rewritten as four X power of 3/2 minus one in the exponent, which would be four X to the power of one half. So our proper rewriting could be considered to be for root X. Then we're asked to differentiate. So we can we can write the differentiated step as 1/2 times four times X power of negative 1/2. which can be simplified down to two over route X.

Wow in this problem we want to find the derivative of the function. Why equals four X. The negative three. So this question is challenging an understanding of the derivative in particular how to find the derivative of a function using different shortcuts rather than the traditional limit definition we find previously. So to solve what we need to do is use the shortcut that we've gained. These are one through six. The constant rule, multiple rule, power rule, trade rules, exponential rule and some will, respectively. If we rewrite why? In a more easily differential form we can solve using these rules. So rewriting we have why equals four X. The third. Four over extensive. Third is equivalently four times X to the positive three. So we see that we can use the multiple rule in conjunction with the power role. Now to solve thus we have D I d X equals four times dx execute, which is four times three X squared by the power rule. Thus we simplify as dy dx equals 12 X square

For this problem, we are asked to complete the tables shown where we are given the original function Y equals four over X power of negative three. Next step is to rewrite this where we'll note that dividing by X power of negative three is the same thing as multiplying by X to the power of three. So next step is to differentiate. So taking the derivative with respect to X, we would have three. That was an awful three. We have three times four X squared. And then simplifying, we can see that we have Y prime equals 12 X squared.

For this problem, we are asked to complete the table shown without using the quotient rule. Starting with the function for over five X squared, You can rewrite this as 4/5 times x the power of -2. Then differentiating, we'll get negative two times 4/5 Times x power of -3, which means that we can simplify this down into the form negative 8/5 X cubed.


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