5

1. Find dy for the following: dc (a) y = (722 32 + 15)2 (b) y = cot 7 31 (c) y = e tan 151(d) y = cos (sin 30.) (e) f(z) = sin 4(22) (f) g(2) = 25ln l6x 727 02? (g...

Question

1. Find dy for the following: dc (a) y = (722 32 + 15)2 (b) y = cot 7 31 (c) y = e tan 151(d) y = cos (sin 30.) (e) f(z) = sin 4(22) (f) g(2) = 25ln l6x 727 02? (g) y =

1. Find dy for the following: dc (a) y = (722 32 + 15)2 (b) y = cot 7 31 (c) y = e tan 151 (d) y = cos (sin 30.) (e) f(z) = sin 4(22) (f) g(2) = 25ln l6x 727 02? (g) y =



Answers

(a) Find the differential $ dy $ and (b) evaluate $ dy $ for the given values of $ x $ and $ dx. $
$ y = \cos \pi x, x = \frac {1}{3}, dx = -0.02 $

In the question, they are asking to find a differential device in a an inferior century value divide for the given values of eccentrics. So Why is equal to tonics given in the question? And the x equal to fiber forgives equal 2.1. So four questions a why equal to tonics given in question given the question. And therefore the differential divide will be equal to sex square D X six square X D X. This is the answer for question. A and in question be when X equal to by by four and the X is equal to minus 40.1. Then divide will be equal to sick of bye bye four whose square into minus 40.1 is equal to route under 200 square into minus 2000.1. So this is equal to minus points to. And this is the answer for the given question And so called 2nd part of this question. And disaster for questioning. Yeah.

This time they want us to find the derivative of sign of X times, cause I know Rex Were any of the product role for this one too? Um, take the route of of the first time. So we have coastline squared X, then leave the second term alone. So we have minus signs. Greater wreck. So it's familiar. This is actually just co sign of two times the angle I get me.

This time they want us to take the derivative of this function well. He considered as coastline of Rex times one over the sine of X plus one. So take the derivative of the 1st 1 I believe the 2nd 1 alone, we get negative Sign ox over its nine X plus one. Then leave the 1st 1 alone. But take the derivative of the second function. So we have negative over one plus sine X squared times the derivative of the inside which is just coast I interacts. So we end up with white crime is equal Teoh Negative sign of Rex Sign of Rex plus one Subtract coastline squared X one plus sign A wreck squared Okay, so we can do a little bit of simplifying serial. It takes us because it doesn't like to clean it out. What amount of light? A top and bottom of this of sign of ax Plus one negative sign of X over sign of X plus one squared And now we can bring the other term with it. Coastlines where Durex. So we end up with Let's see negative sine squared x on its coastline squared X minus sine x Well What is this? We know a triggered anti science squared plus coastline squared is equal to one. So we factor out that negative and just get a one. The sign plus one squared We end up with Let's Negative one plus sign a Rex over a sign of X plus one. So one of these kinds of out and we just have negative 1/1. Plus I know Rex.

So this section is a little bit of a review we're looking at. Here is where we have to To problems that we're focusing on. The first one is really We're looking for the derivative of why equals four X to the third minus seven X squared and we're looking at why equals X times the coastline of X. So in this case, what we're going to do here is I'm going to take the derivative of both sides and I could do implicit differentiation as well here, which is nice, but we're just do it regular. So we'll do. D Y d x, which is the derivative, is equal to 12 x squared minus 14 X bringing the act DX over. I'm gonna find out that the differential will be 12 x squared minus 14 acts DX. So finding the differential here, we have to use the product. So we have de Y d X is equal to the first times the derivative of the second plus the second times the derivative of the first. So in this case, if I clean this up, do you Why will equal negative x sign of X lost the coastline of axe on parentheses DX


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