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Find the derivative of the function_f(x) (4x _ Sx2 + 4)-3/2...

Question

Find the derivative of the function_f(x) (4x _ Sx2 + 4)-3/2

Find the derivative of the function_ f(x) (4x _ Sx2 + 4)-3/2



Answers

Find the derivative of the function.
$f(x)=x^{2}-3 x+4$

Okay this time, Like it was the function X times for to the three expired. And while that change this expressions of submitting all we end the full report for its extreme than the fours before. So we have I am for the more. And now we can do the product girl either of the first time leave Second term alone's away at one time for to the and then I'll leave the first term alone. Take the derivative of the second term. And as we saw before here and that in the front. And this is my rewrite that to be a bit, uh, towards the I guess we could factor out this all right? Yeah.

It was the function after Lex is equal to X times for three to the X. Well, let's see. First, let's hearings that a little bit for cubed to the X Power. Well, this is equal to x times that c 64 to the X. Now let's do the product. We can take the derivative of the first factor. So it just gives the one times the second factor left alone. And now we'll do the opposite. Will leave the first factor. Don't you think that they're the second? But as we saw in the previous question, that's just natural. Log 64 Time 64 It's on the X. We could factor out if you wanted to the 64 to the X. All those is fine. You'll end up with 64 to the X and then one plus the natural log of 64 times X. Okay,

All right. We want to find the derivative of a given function which is why equals four X cubed plus three X squared over asks. This question is challenging our basic understanding of derivative in particular, how to find derivatives using shortcuts instead of the traditional limit definition we learned previously. So in order to solve we need to rely on the following shortcuts one through six respectively. These are the constant rule, multiple rule, power rule trigger rule, exponential rule in some rule. So we see that our function can be written as Y equals four X squared plus three actors distributing the knowledge for each of the terms of room reader. Thus we can take each of these two derivatives. One by one is in the sum rule where for each term we use both multiple rule and the power rule two and three. So with this in mind we have do I. D x equals four times to actually first plus three times one extra zero, which is simply a X plus three.

In the given question we have to find derivative or effects. It was true 4 -3 Access Square. By the help of limits. So to find the There you will too we have formula that days LTD tends to zero F of explicit minus a pocket divided by it. Yet I am providing all the values. Well you're function it Explicit is 4 -3. Hindu explicit foley square minus value of function. It vaccines 4 -3 Access where the world by age. No Your four those guns allowed. OK now I am going to take minus three as common and you should get explosive police where minus access were divided by H. Okay, after that if we open the holy square then you can say that literally provide you access where the city square let's do exit and uh minus of access square divided by catch your access square goals, cancel out after that into the remaining terms. We can take a chess common after that It converts into at Plus two works divided by touch. Now you're Rachel's looking too loud. No, finally you get limited, tends to zero minus three X plus two. Works. So after putting the limit with that -3, multiplied by two weeks means minus six X. So this is my final answer Of the one question that is -6x. Okay, thank you.


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