MisterPants
Senior member
I'm a jackass, and I can't differentiate. I'll have to use dw/dt, etc to denote partials because i don't have curly ds.
x=rcos(t). Show that dw/dx=(dw/dr)cos(t)-(dw/dt)(sin(t)/r)
My flawed solution:
dw/dx=(dw/dr)(dr/dx)+(dw/dt)(dt/dx)
r=x/cos(t), dr/dx=1/cos(t)
x=rcos(t), dx/ds=-rsin(t)(dt/ds), dt/dx=-1/rsin(t)
dw/dx=(dw/dr)(1/cos(t)) - (dw/dt)(1/rsin(t))
x=rcos(t). Show that dw/dx=(dw/dr)cos(t)-(dw/dt)(sin(t)/r)
My flawed solution:
dw/dx=(dw/dr)(dr/dx)+(dw/dt)(dt/dx)
r=x/cos(t), dr/dx=1/cos(t)
x=rcos(t), dx/ds=-rsin(t)(dt/ds), dt/dx=-1/rsin(t)
dw/dx=(dw/dr)(1/cos(t)) - (dw/dt)(1/rsin(t))
