https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:untitled-929/v/calculus-derivative-of-x-x-x 2025-08-25T11:24:50.796694667Z संयुक्त चरघातांकी फलन अवकलन (differentiation) Sal finds the derivatives of xˣ and x^(xˣ). They are surprisingly fun to do! Sal Khan video https://cdn.kastatic.org/googleusercontent/0MpzPWEFfcYegqyHgzckEEX6dsbhs67DvnMKkF6MDeTmZ99uF4jAe14qc6F2tFEgg4hDzyaqIW03Er0OI-Z9eRnM संयुक्त चरघातांकी फलन अवकलन (differentiation) Sal finds the derivatives of xˣ and x^(xˣ). They are surprisingly fun to do! https://cdn.kastatic.org/ka-youtube-converted/N5kkwVoAtkc.mp4/N5kkwVoAtkc.mp4 542 लघुगणकीय अवकलन https://hi.khanacademy.org/math/ncert-class-12/x7ce8ca9c5869750b:continuity-and-differentiability-ncert-new/x7ce8ca9c5869750b:untitled-929/e/logarithmic-differentiation 2025-06-25T04:37:22.958747522Z संयुक्त चरघातांकी फलन अवकलन (differentiation) ऐसे फलनों का अवकलन (differentiation) करें जिनमें चर (variable) आधार और घातांक (exponent) दोनों में हो। उदाहरण के लिए, xˣ का अवकलन करें। Tomer Gal exercise https://hi.khanacademy.org/math/revision-term-1-ncert-math-class-12/x6a634f0b79812b7f:week-2/x6a634f0b79812b7f:continuity-and-differentiability/v/log-differentiation-of-implicit-functions 2025-06-25T04:37:22.958747522Z अस्पष्ट फलनों का लघुगणकीय अवकलन In this video, we learn how to perform logarithmic differentiation of implicit functions. We first look at the function x^y = y^x and then pick up (cosx)^y = (cosx)^y. In both of these, the powers can be brought down using properties of log. This is what makes logarithmeic differentiation a useful too for situations like these. Once we've dealt with the powers, we can use product rule and chain rule to perform the differentiation. Once this part is done, we can readily isolate dy/dx. Ashish Gupta video https://cdn.kastatic.org/googleusercontent/ZCdwTudJg6e6n-P2gsaUborP4izvMsGo71pvEVlX9dNYWcLXcP7VHkWpn2grt4TUP1KoJLQP9NswyHBuBLSFTBw अस्पष्ट फलनों का लघुगणकीय अवकलन In this video, we learn how to perform logarithmic differentiation of implicit functions. We first look at the function x^y = y^x and then pick up (cosx)^y = (cosx)^y. In both of these, the powers can be brought down using properties of log. This is what makes logarithmeic differentiation a useful too for situations like these. Once we've dealt with the powers, we can use product rule and chain rule to perform the differentiation. Once this part is done, we can readily isolate dy/dx. https://cdn.kastatic.org/ka-youtube-converted/p-UO_t_XvPI.mp4/p-UO_t_XvPI.mp4 476 लघुगणकीय अवकलन