Find the derivative of
(i) $2 x-\frac{3}{4}$
(ii) $\left(5 x^{3}+3 x-1\right)(x-1)$
(iii) $x^{-3}(5+3 x)$
(iv) $x^{5}\left(3-6 x^{-9}\right)$
(v) $x^{-4}\left(3-4 x^{-5}\right)$
(vi) $\frac{2}{x+1}-\frac{x^{2}}{3 x-1}$

Answer

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Calculus 1 / AB

NCERT Class 11 - Math

Chapter 13

Limits and Derivatives

Section 2

Coordinate Axes and Coordinate Planes in Three Dimensional Space

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Video Transcript

So in this question we are given certain functions and we need to find the differentiation of those Had to start from the first function which is given to be two X -3. Before we need to find the differentiation of dysfunction. So divided by DX will be D by D X. Of this whole function. Okay so there is a subtraction of over there so we can just split it up in two different parts. That is the body X. Of two, X minus the body X. Of three by four. Okay so divide the X. Of two. X is two and divide the X of a constant value is zero. So the answer comes out to be zero. Now moving on to the 2nd part, Second part contains a function which is by equals two five x cube plus three x -1 And two X -1. Okay here we can use the you will you will you will say that they buy the eggs of UV Z equals two B. By the eggs of U. And V. Remains as it is plus you and be by the eggs of we. Okay this is the usual. So we'll use this rule. This is also all this product rule. So they use this. So the by the X of Y will become derivative of this function. The derivative of this function is nothing but 15 X squared plus three. While the applied dysfunction remains as it is. Plus the first functions remains as it is And the derivative of the second function will be one. Okay so now every just solve it. We just simplify it. It becomes 20 X. Q -15 x squared last 66 minus poor. Okay so this is the derivative of second function. Now let's move on with heart function. Third function contains by equals two extra depart -3 and 25 plus three X. Okay so either we can use your rule or we can multiply extra people minus three inside. So it becomes extra two by minus three plus three Extra Dubai Ministry. Now there is an additional over there so we can split this up. So this is why and then Bangladesh becomes five and derivative of five extra depart -3 it is five and 2 -3 and it works to the par -4 Plus three and 2 -2 and two extra depart -1 Shot Extra two x -3. So it becomes -15 divided by extra depart four plus minus -6 Divided by Extra Depart. Cute. Okay so this is that deliberative of heart function. Now let's move on to the world function. Court function is by equals two extra depart five. Multiply by three and 26 extra depart minus name. It is pretty similar to the previous part. We just multiply extra. Part five. Inside out it becomes this and if we take the derivative both side It becomes nothing but three and to five extra depart four plus six and +24 because minus minus becomes plus and the para minus five. So the function comes out to be 15 next to the past four divided by 24 x to the path. Right okay Now let's see the 5th part of the question. The part contained the function which is by equals two extra 2 x -4 and took three into four extra by -5. It is also similar question it becomes this and Now we'll take the derivative, it becomes three in 2 -4 extra depart -5 And Plus four into 9 and two extra depart -10. Okay so the answer comes out to be minus 12, extremely bad minus six Plus 36 extra. The par -11. Okay you can notice that these questions are pretty similar so you can just solve it out using the product rule or either the change rule. Okay these are pretty simple. Now let's move on to the last part. Last part is nothing but why equals two shoddy last part is by equal strips two divided by X plus one minus X squared divided by three x minus one there. You can see that there is a minus over there so we can split these parts up but you can see that X plus one isn't the denominator. Okay so either you can use you by the rule. There is a you by the rules okay? Which says that the by the X. Of you by the is we squared and the by the eggs of you and we remains as it is minus you remains as it is and D by D. X. Of be okay. Either you can use this rule or you can just see use product rule where the other products become one. By x minus X plus one. Okay so we'll use this division rule. So my dish becomes X plus one. What? And to the baby X. Of They were the eggs of two -2 remains as it is and the body kicks off Express why? Well they're divided by X plus one whole square. Okay and just see the second part, if you see the second part it is minus of three x plus one. So it's pre X -1. Mhm. And the by the X. Of X squared minus experiments as it is. And the body exhaust three x plus one and in the region what we have is three x -1 whole square. Okay now we just need to simplify this after simplifying what we get is gardez equals to four stomach zero minus two divided by X plus one whole square. Okay and next thomas three X plus three X minus one and 22 x minus x squared and 23 divided by Divided by three x -1 old square. Okay so this is our answer. You can just simplify it if you want. I'll just simplified for you. It becomes minus two divided by X plus one old square minus three X squared minus two X Divided by three X -1 Whole Square. And if you absorb it becomes -1 divided by Express 1 to the path, two -X and 23 x -2 divided by three x -1 old square. Okay that's it. Thank you.

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