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Vx+I(x' + 5)l y = Sx + In x2 + 6Find the derivative_...

Question

Vx+I(x' + 5)l y = Sx + In x2 + 6Find the derivative_

Vx+I(x' + 5)l y = Sx + In x2 + 6 Find the derivative_



Answers

Find the derivative of the algebraic function. $$f(x)=\frac{x^{2}+5 x+6}{x^{2}-4}$$

Yeah. In this problem we want to find the derivative of the given function. Why is equal to X times six to the negative two X. Power. This question is challenged understanding of how to find the derivative of a function. In order to solve, we have to understand how to find derivatives for both. Exponential derivative with non basic E. As well as the product. So we also need to know how the chain rule which states A. D. D. Accept. You accept Dfd you Fergie time. GTX. This is used for compound functions as 1/6 or negative two. X. We note that for compound functions when using the general we can also apply differentiation, shortcuts, parallel products and so on and can readily using approach. So why is already written in its most easily defensible form? We note that D D x eight of the year with a day of the year, the U D X L N. A. We have to use the product rule for 16 negative two X 86. Us negative two X. So we have dY DX 66 to the negative two X plus x x negative two x l n six minus two or 60 negative two x times one minus two x l n six.

Question is y equals 2 6 to the power five. We have to differentiate this with respect to X. Firstly we will use change rule to differentiate it is it changed? So according to the change do we can say if we have to differentiate the body itself? If E X. Then it can be return isn't F dish E X. Judicial X. There I can see then F X is equal to 6 to the power of x. And G X is five X. Now we will solve this by applying this change so can we applying this chain rule Let that 5X is equal to you. So we can write it divide the you of 6 to the power you because in place of five minutes I have put you Into DVD exhaust five x. Now differentiating by using the explanation rule. It can be written as the where do you off? It is the power you is reno here to the power you log. So we're in discussion Is equal to six. So we will use this identity to solve discussion. So it can build tennis 6 to the power you Law six. And remaining parties divide the eggs of five eggs. Further solving discussion. It can be re tennis Six to the power. When we air. When we again with the value of you, which is five X. six. To the power five x. Log six. And differentiation of five X. It means finally I get. The answer is videsh equals 25 Multiplied 6 to the power five eggs. Law six. So you can see this is the final answer after differentiation.

Hi. Today we will be solving the following problem. I need derivative off W Why? Which is defined as six times y to the power four plus seven times y to the power of two thirds. Now who saw this problem? Let's review the power rule taking derivatives. That is, if you want to take me during the function and I can sing to find I'm taking the derivative with respect to X pricing ttx off they function x to the power fi he derivative of Except horrify is going to be high times X to the power of I minus one. Now we have a constant before X any value so we can write that out by saying the derivative or ddx of some constant C times X to have heart I and note that X is a variable, while I and Sea air with constant numbers the derivative off. That would be see Time's D D acts according to the derivative with respect to X of X to the party. And this is because the value of seas Constance, who doesn't change with X so you can move outside of the derivative and that would be equal to see times I time's acts to the power ofthe eye minus one. Now we can use these principles to solve for the derivative of w fl y. You know, when my examples I used the variable X But since we're taking the deer made with respect to why the prose was the exact same thing but was just different and it was a different name for the variable. Oh, so look table to fall this stuff over here and start solving court are derivative off w off. Why? Okay, so we have a W for rising to six times why? To par four plus seven times y to the power of two thirds. So the derivative w y, and I conclude an apostrophe here to signify that I'm taking the first derivative is equal to So first, let's take the derivative of six times White have power for core here eating the power will. It would be six times four off. Why? To the power of four minus one Sold three. Now let's take the derivative of seven times. Watch part two thirds. So he dirt of seven times while his heart two thirds his seven times two affairs time to y to the power two thirds minus one. So we just negative one third that we can simplify this further and say six times. Forest twenty four. So we have twenty four. Why? To power three and then seven times two thirds. He's equal to fourteen over three. Why? To the power of negative one third. And that's it. There's preservative, huh? W off. Why, thank you for watching.

All right, We are asked to find the derivative of this composition function two times a quantity of X cubed plus six to the fifth power. And as I mentioned, it's a composition function. So you have an inner function with an outer function, which is your clue that you're going to do the chain rule. So what you do is a derivative of the outer function. First, that's the two something to the fifth. So you bring that five in front two times five is 10. Subtract one from your exponents. You leave the inner function alone and you multiply by the drift of of the inter function. Well, the drift of of X cubed is three x squared and the derivative of 60 So nothing to do there as far as simplifying ghosts, multiplication communities. So you can you can move this three x squared in front. Um, Times 10 is 30 x squared and, yeah, just leave everything else alone and you're done Mhm


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