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Category: Differentiation

find-the-n-th-derivative-of-function-y-sin-x-by-Leibniz-theorem-

Question Number 85169 by jagoll last updated on 19/Mar/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{derivative}\:\mathrm{of}\:\mathrm{function} \\ $$$$\mathrm{y}\:=\:\sqrt{\mathrm{sin}\:\mathrm{x}}\:\mathrm{by}\:\mathrm{Leibniz}\:\mathrm{theorem} \\ $$ Commented by mr W last updated on 19/Mar/20 $${i}\:{don}'{t}\:{think}\:{Leibniz}\:{theorem}\:{helps} \\…

Solve-the-differential-equation-1-x-xy-2-dy-y-y-3-dx-

Question Number 85111 by niroj last updated on 19/Mar/20 $$\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equation}}: \\ $$$$\:\bigstar.\left(\mathrm{1}+\mathrm{x}+\mathrm{xy}^{\mathrm{2}} \right)\mathrm{dy}+\left(\mathrm{y}+\mathrm{y}^{\mathrm{3}} \right)\mathrm{dx} \\ $$$$\: \\ $$ Commented by jagoll last updated on 19/Mar/20…

The-function-f-x-e-x-x-being-differentiable-and-one-to-one-has-a-differentiable-inverse-f-1-x-The-value-of-d-dx-f-1-at-point-f-ln-2-is-

Question Number 150594 by liberty last updated on 13/Aug/21 $$\mathrm{The}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{e}^{\mathrm{x}} +\mathrm{x}\:\mathrm{being} \\ $$$$\mathrm{differentiable}\:\mathrm{and}\:\mathrm{one}\:\mathrm{to}\:\mathrm{one}\:, \\ $$$$\mathrm{has}\:\mathrm{a}\:\mathrm{differentiable}\:\mathrm{inverse}\:\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right). \\ $$$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\frac{{d}}{{dx}}\:\left({f}^{−\mathrm{1}} \right)\:\mathrm{at}\:\mathrm{point}\: \\ $$$$\mathrm{f}\left(\mathrm{ln}\:\mathrm{2}\right)\:\mathrm{is}\:\_\_ \\ $$ Answered by…

Let-g-is-the-inverse-function-of-f-and-f-x-x-10-1-x-2-If-g-2-a-then-g-2-

Question Number 150590 by liberty last updated on 13/Aug/21 $$\mathrm{Let}\:\mathrm{g}\:\mathrm{is}\:\mathrm{the}\:\mathrm{inverse}\:\mathrm{function}\:\mathrm{of} \\ $$$$\mathrm{f}\:\mathrm{and}\:\mathrm{f}\:'\left(\mathrm{x}\right)=\frac{\mathrm{x}^{\mathrm{10}} }{\mathrm{1}+\mathrm{x}^{\mathrm{2}} }.\:\mathrm{If}\:\mathrm{g}\left(\mathrm{2}\right)=\:{a}\:\mathrm{then} \\ $$$$\mathrm{g}\:'\left(\mathrm{2}\right)\:=\_\_\: \\ $$ Answered by Olaf_Thorendsen last updated on 13/Aug/21…

lim-x-0-x-sin-x-x-5-2-

Question Number 84954 by john santu last updated on 17/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{\mathrm{x}}\:−\:\sqrt{\mathrm{sin}\:\mathrm{x}}}{\mathrm{x}^{\frac{\mathrm{5}}{\mathrm{2}}} }\:=\:? \\ $$ Answered by john santu last updated on 17/Mar/20 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{x}−\mathrm{sin}\:\mathrm{x}}{\mathrm{x}^{\mathrm{2}}…

prove-that-0-1-2-m-n-

Question Number 150226 by mnjuly1970 last updated on 10/Aug/21 $$ \\ $$$$\:\:\:\:\:\mathrm{prove}\:\:\mathrm{that}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\zeta\:\left(\mathrm{0}\:\right)\overset{?} {=}\:\frac{−\mathrm{1}}{\mathrm{2}}\:……….\blacksquare \\ $$$$\:\:\:\:\:\:\:{m}.{n}… \\ $$ Answered by Kamel last…