Math (Calculus)

posted by .

this is a question I don't understand:

Demonstrate the following derivative rule:

(Arccsc(u))' = (-1/u(u^2-1)^1/2) * u'

Where u = g(x)

Do they want me to start with (Arccsc(u)) and get to (-1/u(u^2-1)^1/2) * u' ?

Thank you

  • Math (Calculus) -

    That's the idea, but you have to go to it backwards, in a way

    if y = arccsc(x) then x = csc(y)

    dx/dy = -cscy ctny

    but ctny = sqrt(csc^2 y - 1)

    dx/dy = -x sqrt(x^2 - 1)

    dy/dx = -1/[x * sqrt(x^2-1)]

    If we have y = arccsc(u) then the chain rule says we have

    dy/dx = dy/du * du/dx = -1/[u * sqrt(u^2-1)]

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    can some one please help me with the following questions as i don't understand them please (a) write down the derivative of each of the functions f(x)=E7x and g(x)=cos(2x) using the product rule differentiate the function k(x)=E7xcos(2x) …

    what is the derivative of ln(x-1)? If you are studying the calculus of logarithms your question surprises me, since that is one of the most basic ones in that topic. in general if y = ln("anything") then y' = 1/"anything" * derivative
  3. Trig (inverse functions)

    Problem: tan[arccsc(-5/3) + arctan(1/4)] My work: let arccsc(-5/3)=X and let arctan(1/4)=Y where -pi/2<=X<=pi/2, X cannot be 0 and where -pi/2<Y<pi/2 so that cscX=-5/3 and tanY=1/4 The problem can now be written as tan(X+Y) …
  4. Trigonometry

    In this problem, you will describe in detail how we arrive at the accepted definition of the function y= Arccsc(x) a) Sketch the cosecant function over the interval (-2pi, 2pi) i can do that b) This function is not one to one - please …
  5. Calculus

    find the derivative of f(x)=((x^2+3)^5+x)^2 using the chain rule. I know that I would start with f'(x)=2((x^2+3)^5+x) but I don't know how to do the rest
  6. pre cal\trig

    Find the following cot(Arccsc 25/24) show your work
  7. trig

    cos(arccsc(-20)) Im not allowed to have a decimal answer
  8. Calculus

    y= [(x-3)/(x^2+1)]^2 find the derivative. I know i would start off with the chain rule. but would i then continue on and use the quotient rule next?
  9. Calculus

    1.) Find the derivative of tan (sec x). 2.) Find the derivative if 1/x in four ways, using the limit process, power rule, quotient rule and implicit differentiation. 3.) Show that the derivative of sec^-1 x is 1/(|x|*sqrt(x^2 -1)). …
  10. Math (Calculus)

    Hello, Could somebody please help me with the following question?

More Similar Questions