5

Find y'y = cot (6x 1) 36...

Question

Find y'y = cot (6x 1) 36

Find y' y = cot (6x 1) 36



Answers

Find $y^{\prime \prime}$.
$$y=\cot (3 x-1)$$

Prime for Y equals the co tangent of X over X. Okay. It's certainly a question. So, I'm just gonna go ahead and use the quotient rule. It's the bottom X times the derivative of the top. All right. Um I know the derivative of the tangent is the second squared, so I'm guessing the derivative of the coach. Co tangent is co second squared and it is except for with a minus sign. So minus cosine squared X. So down bottom drifted away at the top, minus the top Times the derivative of the bottom, which is one all over the bottom square, so minus X. Co second squared X minus co tangent X over X squared. I think I just leave it like that. Um I can't think of anything that will make it better looking.

Section 3.6 number 73. So they give me a function and I am tasked with finding the second derivative of this function, which means I have to first find its first derivative. So that is going to be 1/9. The differentiation of the coach engine is going to give me minus co Seacon squared of three X minus one. Now the derivative of three X minus one is just three. So this tells me that this derivative is minus 1/3 so minus 1/3 the coast Seacon squared of three X minus one. So a minus 1/3 coast tickets, girder three, demonic three expense. One is the first derivative. And so now I need to find the second derivative. So the second derivative is going to be minus 1/3 and now I use the power role. So it's co Seacon squared. So that would be too times the coast seek it of three X minus one to the first power. Now I take the derivative of the coast seeking the derivative of the coast. Sequent is just going to be minus Coach Tangent three X minus one Go seek it three x minus one. Now the derivative of three X minus one is just three. And so, if you look at this, you have got to minus signs. I've got a three over a three, and so this simplifies to to and then coast seeking. I've got two of those co seek in squared three X minus one times the co tangent of three X minus one. So that's the final answer to co CK in squared three x minus one co Tens of the three x minus one is the second derivative.

It's called tangent of X. We need to okay, Get the 2nd derivative of this year. I want to do that to take the first derivative. Start with that. So we have why is equal to negative consequent squared X. You don't drive time next. Sweets negative too cosi kit of X threat of negative cosy chat oratory to cozy exes because he can't get a pussy cacs. Tan jacks got that. Actually taking a cozy connects contention next. Yeah. So That gives us two cause he can't square tex contention. X. Sure. I took

Okay, we have. Why is two contingent one over square root of X? If you take the derivative with respect to X, we get negative too. Coast seeking Squared one over, Dex. And then we got a multiply by the derivative of one of the real Lex. Okay, so it's going to be minus one half and then x to the minus three house. So what? One of the relaxes x to the minus the half to the derivative is negative one half x to the much three house uncertainty. Why? Well, this negative two times negative, one half goods away. So we just have because she can't square one ever it x The extra three house we can put in the denominator, Tex, There's the difference anyway.


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