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. 👍 0
  2. 👎 0
  3. 👁 557
  1. I did this for you here:
    https://www.jiskha.com/display.cgi?id=1526060796

    Why are you reposting it ?

    1. 👍 0
    2. 👎 0
  2. It wasn't correct and I wanted to post my answer I got for context

    1. 👍 0
    2. 👎 0
  3. But it is correct.
    Proof:
    http://www.wolframalpha.com/input/?i=find+dy%2Fdx+for+cos(x)+%2B+sqrt(y)%3D+1

    1. 👍 0
    2. 👎 0
  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. 👍 0
    2. 👎 0

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. Calc

    Find y'' by implicit differentiation. 5x2 + y2 = 3 y'' =?

  4. Calculus 1

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

  1. Calculus

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

  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. Calculus

    Consider the following. cos(x) + sqrt(y)= 1 (a) Find y' by implicit differentiation. y' = 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

  4. calculus

    Find the derivative of the function 1)f(t)=tan(e^2t)+e^tan2t f'(t)= [im not quite sure with this. im assuming the implicit differentiation] 2) F(t)=e^(8tsin2t) [for this one i got 2e^(8t)(4sin(2t)+cos(2t)) but it is incorrect.

  1. Math - implicit differentiation

    Suppose 5x^2+2x+xy=2 and y(2)=−11. Find y′(2) by implicit differentiation.

  2. Math

    Find dy/dx by implicit differentiation. cot(y) = 4x − 6y

  3. Implicit differentiation calculus

    PLEASE HELP , I DON'T UNDERSTAND find dy/dx by implicit differentiation a) xy + x^5y^2 + 3x^3 - 4 = 1 b) lny = cos x thank you

  4. calc

    find the area between the x-axis and the graph of the given function over the given interval: y = sqrt(9-x^2) over [-3,3] you need to do integration from -3 to 3. First you find the anti-derivative when you find the

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