Question

\[Given u=e ^{rcos \theta}.\cos(rsin \theta), v=e ^{rcos \theta}.\sin(rsin \theta) prove that du/dr=1/r.dv/d \theta and dv/dr=-1/rdu/d \theta\]

Answer 1

Dipti Do you want the Calculus or Algebra ?

Answer 2

calculus

Answer 3

Okay
\[u = e^{rcosa}*cos(r sina)\]
\[\frac{du}{dr} = cos(rsina)(e^{rcosa} (cosa - rsina\frac{da}{sr})) - e^{rcosa}(sin(rsina)(sina + rcosa\frac{da}{dr}))\]



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Answer 4

\[v= e^{rcosa}*sin(rsina)\]
\[\frac{dv}{da} = e^{rcosa}(cos(rsina(\frac{dr}{da}sina + cosa r)) + sin(rsina)(e^{rcosa}(\frac{dr}{da} cosa - sina r))\]

Answer 5

There you go ..please check them ..

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Answer 6

thanks, i know you hate this problems , but i want the help for answer