5

E' sinly)JysindxCOSJcosdy...

Question

E' sinly)JysindxCOSJcosdy

e' sinly) Jysin dx COS Jcos dy



Answers

Find dy/dx for the following functions. $y=e^{-x} \sin x$

This time they want us to find that relative of the function wise equal to eat. Six x Santa. Let's do you predict role. Take the derivative of the first time really, with 2nd 1 alone. Then leave the first term alone and take the derivative of the second term. And this is ah, derivative six and Iraq's plus goes on your ex.

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.

All right. In this problem we wish to find the derivative of Primack for the function F X equals X over x minus cosine X. This question is challenging understanding of differentiation in particular, is challenging our newfound knowledge of the trigonometry derivatives needed a 600 listed here. DDX in Mexico Cenex the exports index is negative. Sine X Dx candidacy can squared dX coach engine is negative close to camp squared DT Xz can't see can't tangent and DDX coast is negative coast. You can't go changing. So listen it. In order to solve, we need to utilize these six trigonometry derivatives in conjunction with previous techniques we've learned namely because probably you just legalize the quotient rule because we've divided by Sine X minus cosine X by the quotient rule, F prime X is as I simplified here, DDX 1/1 over Sine X and x minus 1/1, which simplifies the GTX 1/1 minus X. Thus F prime X is zero minutes. Go to the next minus cosine squared X times 1/1 minus cosine X squared which simplifies as negative coast. You can't squared X over one minute coach engine X squared

This time they want us to find the derivative of sign of X the SCO Zion A rex. Okay, where y is a function of it So we can do the white over. The X is equal to well, they're differentiation is linear, so we can take the derivative of each time individually may get coastline Rx minus sign of banks


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