{"id":7871,"date":"2021-11-09T19:11:23","date_gmt":"2021-11-09T13:41:23","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7871"},"modified":"2021-11-09T19:26:34","modified_gmt":"2021-11-09T13:56:34","slug":"what-is-the-differentiation-of-log-sin-x","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-differentiation-of-log-sin-x\/","title":{"rendered":"What is the differentiation of log sin x ?"},"content":{"rendered":"
We have, y = log sin x<\/p>\n
By using chain rule in differentiation<\/a>,<\/p>\n Let u = sin x \\(\\implies\\) \\(du\\over dx\\) = cos x<\/p>\n And, y = log u \\(\\implies\\) \\(dy\\over du\\) = \\(1\\over u\\)\u00a0<\/p>\n Now, \\(dy\\over dx\\) = \\(dy\\over du\\) \\(\\times\\) \\(du\\over dx\\)<\/p>\n \\(\\implies\\) \\(dy\\over dx\\) = \\(1\\over u\\) \\(\\times\\) cos x<\/p>\n \\(\\implies\\) \\(dy\\over dx\\) = \\(1\\over sin x\\) \\(\\times\\) cos x = cot x<\/p>\n Hence, the differentiation of log sin x with respect to x is cot x.<\/p>\n What is the differentiation of 1\/log x ?<\/a><\/p>\n What is the differentiation of \\(log x^2\\) ?<\/a><\/p>\n What is the Differentiation of x log x ?<\/a><\/p>\n
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