Calc

Consider the following.
cos(x) + sqrt(y)= 1

(a) Find y' by implicit differentiation.
y' = 2y^(1/2) sin(x)
Correct: Your answer is correct.

(b) Solve the equation explicitly for y and differentiate to get y' in terms of x.
y' = ?

(c) Check that your solutions to parts (a) and (b) are consistent by substituting the expression for y into your solution for part (a).
y' =?

  1. 👍
  2. 👎
  3. 👁
  1. I did this for you here:
    https://www.jiskha.com/display.cgi?id=1526060796

    Why are you reposting it ?

    1. 👍
    2. 👎
  2. It wasn't correct and I wanted to post my answer I got for context

    1. 👍
    2. 👎
  3. But it is correct.
    Proof:
    http://www.wolframalpha.com/input/?i=find+dy%2Fdx+for+cos(x)+%2B+sqrt(y)%3D+1

    1. 👍
    2. 👎
  4. cos(x) + sqrt(y)= 1
    -sin x dx/dx + (1/2) y^-.5 dy/dx = 0
    dy/dx = 2 sin x /y^-.5 = 2 sin x sqrt y
    so it is surely correct
    cos(x) + sqrt(y)= 1

    sqrt y = 1 - cos x
    y = 1 -2 cos x + cos^2 x
    dy/dx = 2 sin x - 2 cos x sin x = 2 sin x (1- cos x) That is part 2
    but we know that 1 - cos x = sqrt y
    so
    dy/dx = 2 sin x sqrt y (again)
    that shows they are consistent

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Trig

    Find the exact values of the six trigonometric functions 0 if the terminal side of 0 in standard position contains the points(-5,-4). (0 is not the number zero I don't know what its called) I have to find r first. r=sqrt x^2+y^2

  2. re: Differential Calculus

    Write the equation of lines tangent and normal to the following function at (0, π). To find derivative, use implicit differentiation. x^2cos^2y - siny = 0 Note: I forgot the ^2 for cos on the previous question. Sorry.

  3. Calculus 1

    If 5x^2+5x+xy=2 and y(2)= -14 find y'(2) by implicit differentiation

  4. Trig(3 all with work)

    1)Find the exact value of cos 105 by using a half-angle formula. A)sqrt 2 - sqrt 3 /2 B)-sqrt 2 - sqrt 3 /2 C)-sqrt 2 + sqrt 3 /2 D)sqrt 2 + sqrt 3 /2 cos 105 cos 105 = cos 210/2 sqrt 1 + 210/2 sqrt 1 + sqrt 3/2 /2 sqrt 2 + sqrt

  1. calculus 1

    Please help !!!!! Find dy/dx by implicit differentiation. (sin πx + cos πy)4 = 65

  2. Calculus

    Find dy/dx by implicit differentiation: x^2-2xy+y^3 = c Thank you!

  3. Calculus

    cot(y) = x − 4y Find using implicit differentiation

  4. Calculus

    Find dy/dx of 3 sin x cos y = 2 using implicit differentiation.

  1. calculus

    Given y^4 -x^4=16 find and simplify d2y/dx2 using implicit differentiation. I got the first derivative which was x^3/y^3 and no im am stuck on using implicit differentiation for the second derivative part

  2. calculus

    A. find y' by implicit differentiation. B. solve th equation explicitly for y and differentiate to get y' in terms of x. cos (x) + √y = 5

  3. cal

    Find dy/dx by implicit differentiation given that tan(4x+y)=4x

  4. calculus

    Find dy/dx by implicit differentiation. arctan(2x^2y)=x+4xy^2

You can view more similar questions or ask a new question.