To find d^2y\/dt^2, we need to take the second derivative of y with respect to t:<\/p>\n
dy\/dt = b cos t (using the chain rule)<\/p>\n
d^2y\/dt^2 = -b sin t<\/p>\n
Now, to find d^2y\/de^2, we can use the chain rule again:<\/p>\n
d^2y\/de^2 = d\/dt (d\/dt (y)) \/ (de\/dt)^2<\/p>\n
Since x = a cos t, we can find dt\/de:<\/p>\n
dt\/de = 1 \/ dx\/dt = 1 \/ (-a sin t) (using the chain rule)<\/p>\n
(de\/dt)^2 = (-a sin t)^2<\/p>\n
Now, we can substitute the expressions for d^2y\/dt^2 and (de\/dt)^2:<\/p>\n
d^2y\/de^2 = d\/dt (-b sin t) \/ (-a sin t)^2 = b cos t \/ (a^2 sin^2 t)<\/p>\n
So the final answer is:<\/p>\n
d^2y\/de^2 = b cos t \/ (a^2 sin^2 t)<\/p>\n","protected":false},"excerpt":{"rendered":"
Question: if x=a cos t and y=b sin t, then find d2y\/de2 The correct answer is – To find d^2y\/dt^2, we need to take the second derivative of y with respect to t: dy\/dt = b cos t (using the chain rule) d^2y\/dt^2 = -b sin t Now, to find d^2y\/de^2, we can use the […]<\/p>\n","protected":false},"author":21842,"featured_media":132233,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12119],"tags":[],"class_list":{"0":"post-133943","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-quiz"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133943","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21842"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=133943"}],"version-history":[{"count":1,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133943\/revisions"}],"predecessor-version":[{"id":133944,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/133943\/revisions\/133944"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/132233"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=133943"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=133943"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=133943"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}