Ask a Question
or
Create a Poll
  1. Home /
  2. Questions /
  3. Education And Learning
  4. / Homework
  5. / Studying
  6. / More Studying

by Morman on August 19th, 2008

Morman

Question

Help answer this question below.

Anyone know how to explain why the formula d/dx (inverse sine x) equals 1/[(1-x^2)^0.5]

Share:
Other

Answers. 1 helpful answer below.

  • by bobbinhood on August 22nd, 2008

    bobbinhood

    First, set y between -pi/2 and pi/2. That is, -pi/2 is less than or equal to y, which is less than or equal to pi/2.

    Let y=arcsin(x)
    Then sin(y)=x

    Now differentiate implicitly with respect to x.
    cos(y)y'=1
    y'=1/[cos(y)]

    Because y must be between -pi/2 and pi/2, cos(y) must be nonnegative (greater than or equal to zero).
    Therefore, cos(y) may be written as:
    square root[1-sin^2(y)]
    Substituting x back in for sin(y), we get
    cos(y)=square root[1-x^2]

    Using this substitution for cos(y), we get:
    y'=1/cos(y)
    y'=1/[square root(1-x^2)] provided x is between -1 and 1.

    No comments. Post one | Permalink

Want to attach an image to your answer? Click here.

Did this answer your question? If not, then ask a new question or create a poll.

More Questions. Additional questions in this category.

You're reading Anyone know how to explain why the formula d/dx (inverse sine x) equals 1/[(1-x^2)^0.5]

Follow us on Facebook!

Related Ads

Related Questions

Professionally Researched

ANSWERBAG BUZZ

Formula y b dx
Formula for inverse sine
1 x dx dt
Explain inverse sine
How to explain a formula

Answerbag

a Demand Media company