Results 1 to 5 of 5

Math Help - Partial Differentiation

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    64

    Exclamation Partial Differentiation

    Consider the function f(x,y)=x^2+y^2 where x=sin2θ and y=cos2θ
    df/dθ is given by?

    I know this involves the chain rule and trig id.

    But I'm still not getting it

    Kindly assist.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,325
    Thanks
    10
    Quote Originally Posted by KayPee View Post
    Consider the function f(x,y)=x^2+y^2 where x=sin2θ and y=cos2θ
    df/dθ is given by?

    I know this involves the chain rule and trig id.

    But I'm still not getting it

    Kindly assist.
    Since f is a function of  x \; \text{and}\; y and x \; \text{and}\; y are functions of \theta, then f is a function of \theta so \frac{df}{d \theta} makes sense. The chain rule is

    (1)\;\;\;\;\;\frac{df}{d \theta} = \frac{\partial f}{\partial x} \frac{d x}{d \theta} + \frac{\partial f}{\partial y} \frac{dy} {d \theta} .

    So calculate all of the derivatives

    \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{d x}{ d \theta} \; \text{and}\;\frac{d y}{d \theta}

    and substitute them into (1). Finally, use your expressions for x\; \text{and}\; y to get your final answer.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    10,969
    Thanks
    1010
    Quote Originally Posted by KayPee View Post
    Consider the function f(x,y)=x^2+y^2 where x=sin2θ and y=cos2θ
    df/dθ is given by?

    I know this involves the chain rule and trig id.

    But I'm still not getting it

    Kindly assist.

    What does \sin^2{2\theta} + \cos^2{2\theta} equal?

    What is the derivative of a constant?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Jan 2009
    Posts
    64

    answer

    Quote Originally Posted by Prove It View Post
    What does \sin^2{2\theta} + \cos^2{2\theta} equal? one

    What is the derivative of a constant?

    0

    how would these two answers help me arrive at the final answer

    thanks
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by KayPee View Post
    0

    how would these two answers help me arrive at the final answer

    thanks
    Look at your expression for f(x, y). Now look at what Prove It wrote. Join the dots.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: July 26th 2010, 05:24 PM
  2. Partial differentiation
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 4th 2010, 07:54 PM
  3. Partial Differentiation
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 13th 2009, 07:41 AM
  4. Partial Differentiation
    Posted in the Calculus Forum
    Replies: 3
    Last Post: May 25th 2008, 11:59 PM
  5. partial differentiation
    Posted in the Calculus Forum
    Replies: 4
    Last Post: April 26th 2008, 04:17 AM

Search Tags


/mathhelpforum @mathhelpforum