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Category: Differentiation

If-H-n-1-1-2-1-3-1-n-1-n-prove-that-n-1-H-n-ln-2-n-ln-2-2-

Question Number 211594 by mnjuly1970 last updated on 14/Sep/24 $$ \\ $$$$\:{If}\:,\:\:\overset{\:\:−} {{H}}_{{n}} \:=\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}}\:−…+\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{{n}}\:\:\: \\ $$$${prove}\:{that}:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\overset{\:\:−\:} {{H}}_{{n}} −\mathrm{ln}\left(\mathrm{2}\right)}{{n}}=\mathrm{ln}^{\mathrm{2}} \left(\mathrm{2}\right) \\ $$$$\:\:\:\:\:\:\:−−−−−−−−−−\:\:\:\:\:\: \\…

If-1-x-2-1-y-2-a-x-y-then-prove-that-dy-dx-1-y-2-1-x-2-

Question Number 211508 by MATHEMATICSAM last updated on 11/Sep/24 $$\mathrm{If}\:\sqrt{\mathrm{1}\:−\:{x}^{\mathrm{2}} }\:+\:\sqrt{\mathrm{1}\:−\:{y}^{\mathrm{2}} }\:=\:{a}\left({x}\:−\:{y}\right)\:\mathrm{then} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\frac{{dy}}{{dx}}\:=\:\sqrt{\frac{\mathrm{1}\:−\:{y}^{\mathrm{2}} }{\mathrm{1}\:−\:{x}^{\mathrm{2}} }\:}\:. \\ $$ Commented by Frix last updated on 11/Sep/24…

If-f-x-x-2-g-x-sin-x-Then-find-df-dg-

Question Number 211502 by MathematicalUser2357 last updated on 11/Sep/24 $$\mathrm{If}\:\begin{cases}{{f}\left({x}\right)={x}^{\mathrm{2}} }\\{{g}\left({x}\right)=\mathrm{sin}\:{x}}\end{cases}, \\ $$$$\mathrm{Then}\:\mathrm{find}\:\frac{{df}}{{dg}}. \\ $$ Answered by a.lgnaoui last updated on 11/Sep/24 $$\frac{\mathrm{df}}{\mathrm{dg}}=\frac{\mathrm{df}}{\mathrm{dx}}×\frac{\mathrm{dx}}{\mathrm{dg}}.=\:\:\frac{\mathrm{f}^{'} }{\mathrm{g}'} \\…

Question-210248

Question Number 210248 by universe last updated on 04/Aug/24 Answered by mr W last updated on 04/Aug/24 $$\mathrm{f}''\left(\mathrm{x}\right)>\mathrm{0}\:\Rightarrow\mathrm{f}'\left(\mathrm{x}\right)\:{is}\:{strictly}\:{increasing}. \\ $$$${case}\:\mathrm{1}:\:\mathrm{f}'\left({x}\right)<\mathrm{0} \\ $$$$\Rightarrow{f}\left({x}\right)\:{is}\:{decreasing} \\ $$$${x}+{f}'\left({x}\right)<{x}\:\Rightarrow{f}\left({x}+{f}'\left({x}\right)\right)>{f}\left({x}\right) \\…

If-f-x-x-x-x-find-d-dx-f-x-

Question Number 209924 by OmoloyeMichael last updated on 26/Jul/24 $$\boldsymbol{{If}}\:\:\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)=\left(\boldsymbol{{x}}!\right)\centerdot\left(\boldsymbol{{x}}!!\right)\centerdot\left(\boldsymbol{{x}}!!!\right)\:\: \\ $$$$\boldsymbol{{find}}\:\:\frac{\boldsymbol{{d}}}{\boldsymbol{{dx}}}\left(\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\right)=? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com