这个极坐标的导数怎么求? 极坐标方程求导怎么求?
就是参数方程求导啊,x=acosθ^3
y=asinθ^3
dy/dx=(dy/dθ)*(dθ/dx)=3asinθ^2cosθ/-3acosθ^2sinθ=-sinθ/cosθ,
二阶导道理一样的就是计算麻烦
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绛旓細x琚乧os胃浠f浛锛寉琚乻in胃浠f浛锛屜=鈭(x^2+y^2)浠庤屽緱鍒版柊鐨勬柟绋嬨傝繖鏍风殑鏂圭▼甯稿父鐢ㄦ潵瑙e喅鏇茬嚎闂锛屽妞渾鏇茬嚎銆佺航绾裤佽灪绾跨瓑绛夛紝鍙互浣胯В棰樻洿鍔犳竻鏅扮畝渚裤傝鏇茬嚎C鐨鏋佸潗鏍鏂圭▼涓簉=r锛埼革級銆傚垯C鐨勫弬鏁版柟绋嬩负{ x=r锛埼革級cos胃y=r锛埼革級sin胃鍏朵腑胃涓烘瀬瑙掋傜敱鍙傛暟鏂圭▼姹傚娉锛屽緱鏇茬嚎C鐨...
绛旓細涓鏍风殑绠楁硶銆侱v/D蟻 = -sin蠁/蟻²锛孌v/D蟻 = cos蠁/蟻銆
绛旓細r = a(1+cost) 寰 r^2 = ar(1+cost) = ar +arcost 鍒 x^2+y^2 = a鈭(x^2+y^2) + ax 涓よ竟瀵 x 姹傚锛屽緱 2x+2yy' = a(x+yy')/鈭(x^2+y^2) + a 2x鈭(x^2+y^2)+2yy'鈭(x^2+y^2) = ax+ayy'+a鈭(x^2+y^2)y' = [ax+a鈭(x^2+y^2)-2x鈭...
绛旓細dr/dy=2y/2鈭(x²+y²) =y/r=rsin胃/r=sin胃 浠e叆(2)寰 df/dx=df/dr路(cos胃), df/dy=df/dr路(sin胃)浠e叆(1)寰 df/dr=df/dr路(cos²胃)+df/dr路(sin²胃)=df/dr 瀵兼暟 鏄嚱鏁扮殑灞閮ㄦц川銆備竴涓嚱鏁板湪鏌愪竴鐐鐨勫鏁鎻忚堪浜杩欎釜鍑芥暟鍦ㄨ繖涓鐐归檮杩戠殑鍙樺寲鐜...
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绛旓細sqrt(x^2+y(x)) = a*(1+x/sqrt(x^2+y(x)))-->(1/2)*(2*x+diff(y(x), x))/sqrt(x^2+y(x)) = a*(1/sqrt(x^2+y(x))-(1/2)*x*(2*x+diff(y(x), x))/(x^2+y(x))^(3/2))-->diff(y(x), x) = (-2*x^3-2*x*y(x)+2*a*y(x))/(x^2+...
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