Question

Consider the equation: xsec(y)=y-1
A. compute dy/dx
B compute the slope of this curve at the point (-1,0)

Answer 1

tried part a ?

Answer 2

u know implicit differentiation ?

Answer 3

i know that every time i take a derivative with a y in it ill get dy/dx times it as well. Then i need to group all with dy/dx on one side and the other side group all without them. Then divide to get dy/dx= the answer.

Answer 4

thats almost correct! so whats your attempt in this Q ?

Answer 5

on the left side i need to take the derivative of xsec(y)
so starting with the product rule yes?

Answer 6

yup, go on...i'll stop u when u do any error...

Answer 7

or you could take dx/dy and invert it at the end

Answer 8

you'll need a product rule anyways...

Answer 9

true , but it'll end up with the same answer either way

Answer 10

Alright well taking x'sec(y) 1sec(y)+ x*sec(y)'
so you get sec(y)+(dy/dx)xsec(y)tan(y) right?

Answer 11

yes, and on right ?

Answer 12

the derivative of y-1 is just 1(dy/dx) right?

Answer 13

yes .. now group the dy/dx terms to one side of the equation

Answer 14

doing good job! go on..

Answer 15

so
sec(y)=(dy/dx)-(dy/dx)sec(y)tan(y)
factoring out dy/dx you get
sec(y)=dy/dx(1-xsec(y)tan(y))
so dy/dx=sec(y)/(1-xsec(y)tank(y))?

Answer 16

seems correct.

Answer 17

for B , slope is dy/dx at the specifies point

Answer 18

specified*

Answer 19

you just need to put x=-1, y=0 in dy/dx you got.

Answer 20

So the slope is 1

Answer 21

yes.

Answer 22

Thank you very much for your help

Answer 23

welcome but you did all the work ! :)