# Derivative

What is the derivative of this

y= 1/sin^2x - 2/sinx

1. 👍 0
2. 👎 0
3. 👁 57
1. let z = sin x
dz/dx = cos x

then we have
y = 1/z^2 -2/z

dy/dz = -2z/z^4 + 2/z^2
= -2/z^3 +2/z^2

dy/dx = dy/dz*dz/dx
= (-2/z^3 +2/z^2)cos x
= -2cosx/sin^3x + 2 cos x/sin^2x
=-2 cos x/sin^3x + 2 cos x sin x/sin^3x
= (2 cos x /sin^3x)(sin x - 1)

1. 👍 0
2. 👎 0
posted by Damon

## Similar Questions

1. ### calculus

Could someone check my reasoning? thanx Find the derivative of the function. sin(sin[sinx]) I need to use the chain rule to solve. So I take the derivative sin(sin[sinx) first. Then multiply that by the inside which is the

asked by XCS on May 7, 2009
2. ### Trig Help

Prove the following: [1+sinx]/[1+cscx]=tanx/secx =[1+sinx]/[1+1/sinx] =[1+sinx]/[(sinx+1)/sinx] =[1+sinx]*[sinx/(sinx+1)] =[sinx+sin^2x]/[sinx+1] =[sinx+(1-cos^2x)]/[sinx+1] =??? This is where I'm stuck. Can someone help me.

asked by Anonymous on March 11, 2012
3. ### Is this right

Find the derivative y=sinx(sinx+cosx) I got y'= cos(x)-sin^2(x)+2cos(x)sin(x) is this righttttttt??

asked by Noe on November 11, 2014
4. ### Mathematics - Trigonometric Identities - Reiny

Mathematics - Trigonometric Identities - Reiny, Friday, November 9, 2007 at 10:30pm (sinx - 1 -cos^2x) (sinx + 1 - cos^2x) should have been (sinx - 1 + cos^2x) (sinx + 1 - cos^2x) and then the next line should be sin^2x + sinx -

asked by Anonymous on November 10, 2007
5. ### calc

what is the derivative of sinx- cosy = 0 in its simplest form? I got to the point y'=-consx/siny, but I wasn't too sure. This could probably simplified further. help! You're supposed to treat y as a function of x and differentiate

asked by lil on September 27, 2006
6. ### Math Help

Hello! Can someone please check and see if I did this right? Thanks! :) Directions: Find the exact solutions of the equation in the interval [0,2pi] cos2x+sinx=0 My answer: cos2x+sinx=cos^2x-sin^2x+sinx =1-sin^2x-sin^2x+sinx

asked by Maggie on February 2, 2015
7. ### Math (trigonometric identities)

I was given 21 questions for homework and I can't get the last few no matter how hard and how many times I try. 17. Sinx-1/sinx+1 = -cos^2x/(sinx+1)^2 18. Sin^4x + 2sin^2xcos^2x + cos^4x = 1 19. 4/cos^2x - 5 = 4tan^2x - 1 20. Cosx

asked by Kim on December 4, 2012
8. ### Trig

Simplify sin x cos^2x-sinx Here's my book's explanation which I don't totally follow sin x cos^2x-sinx=sinx(cos^2x-1) =-sinx(1-cos^2x) =-sinx(sin^2x) (Where does sine come from and what happend to cosine?) =-sin^3x

asked by Tara on January 4, 2010
9. ### limits

what is the derivative of e^(3*ln(x^2)) i keep getting 6/x * e^(3*ln(x^2)) but that's not one of the multiple choice so am i doing something wront. also, what is the limit of (1-cosx)/(2*(sinx)^2) as x approaches zero. is the

asked by david on December 9, 2006
10. ### Calculus Help and Check

find the derivative of the function integral from cosx to sinx (ln(8+3v)dv) y'(x)= (sin(8+3((sin(x)))+x)+sin(8+3sin(x)-x))/2 Is this the right answer?????

asked by Chris on May 1, 2014
11. ### Trigonometry.

( tanx/1-cotx )+ (cotx/1-tanx)= (1+secxcscx) Good one! Generally these are done by changing everything to sines and cosines, unless you see some obvious identities. Also generally, it is best to start with the more complicated

asked by mo on April 18, 2007

More Similar Questions