Explore BrainMass

Explore BrainMass

    Partial Derivatives and Appropriate Chain Rule

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Find partial deriv's w/r and w/theta using appropriate chain rule for :
    w=the square root of (25-5x^2-5y^2), where x=r cos theta, y= r sin theta.

    © BrainMass Inc. brainmass.com December 24, 2021, 4:48 pm ad1c9bdddf
    https://brainmass.com/math/derivatives/partial-derivatives-appropriate-chain-rule-9015

    SOLUTION This solution is FREE courtesy of BrainMass!

    w = (25 - 5r^2(cos^2 (theta) + sin^2(theta)))^1/2 or

    w = (25 - 5r^2)^1/2 ( as (cos^2 (theta) + sin^2(theta) = 1)

    therefore dw/dr = 1/2*(25 - 5r^2)^-1/2*-10r or

    dw/dr = -5r*(25 - 5r^2)^-1/2

    dw/dtheta = dw/dx* dx/dtheta + dw/dy * dy/dtheta

    = 1/2((25 - 5x^2 - 5y^2)^-1/2)*-10x*(-r sin(theta))+ 1/2((25 - 5x^2 - 5y^2)^-1/2)*-10y* (rcos(theta))

    Hope it is clear.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:48 pm ad1c9bdddf>
    https://brainmass.com/math/derivatives/partial-derivatives-appropriate-chain-rule-9015

    ADVERTISEMENT