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.
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.© BrainMass Inc. brainmass.com December 24, 2021, 4:48 pm ad1c9bdddf>