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Category: Differentiation

Solve-the-differential-equations-d-2-y-dx-2-x-1-x-2-dy-dx-y-1-x-2-x-1-x-2-

Question Number 91000 by niroj last updated on 27/Apr/20 $$\:\:\boldsymbol{\mathrm{Solve}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{differential}}\:\boldsymbol{\mathrm{equations}}: \\ $$$$\:\:\:\frac{\boldsymbol{\mathrm{d}}^{\mathrm{2}} \boldsymbol{\mathrm{y}}}{\boldsymbol{\mathrm{dx}}^{\mathrm{2}} }+\:\frac{\boldsymbol{\mathrm{x}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }\:\frac{\boldsymbol{\mathrm{dy}}}{\boldsymbol{\mathrm{dx}}}−\:\frac{\boldsymbol{\mathrm{y}}}{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} }=\:\boldsymbol{\mathrm{x}}\sqrt{\mathrm{1}−\boldsymbol{\mathrm{x}}^{\mathrm{2}} } \\ $$ Commented by niroj last updated on…

if-the-value-of-x-is-in-degrees-what-is-the-derivative-of-f-x-sin-x-

Question Number 90881 by  M±th+et+s last updated on 26/Apr/20 $${if}\:{the}\:{value}\:{of}\:{x}\:{is}\:{in}\:{degrees}\:{what}\:{is} \\ $$$${the}\:{derivative}\:{of}\:\:\:{f}\left({x}\right)={sin}\left({x}\right) \\ $$ Commented by mr W last updated on 28/Apr/20 $${we}\:{have}\:{different}\:{understanding}: \\ $$$${if}\:{x}\:{is}\:{in}\:{rad},\:{the}\:{slope}\:\frac{{dy}}{{dx}}\:{is}\:{in}\:{unit}…

n-k-1-n-1-k-1-n-k-H-k-Find-the-value-of-n-1-1-n-1-n-2-

Question Number 156386 by mnjuly1970 last updated on 10/Oct/21 $$ \\ $$$$\:\:\:\:\:\:\:\:\phi\:\left({n}\:\right)=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\left(−\mathrm{1}\:\right)^{\:{k}−\mathrm{1}} \begin{pmatrix}{\:{n}}\\{\:{k}}\end{pmatrix}\:\mathrm{H}_{\:{k}} \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{Find}\:\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left(−\mathrm{1}\right)^{\:{n}−\mathrm{1}} \:\phi\:\left(\:{n}^{\:\mathrm{2}} \right)\:=? \\ $$…

let-a-b-integer-and-C-a-2-b-2-Prove-that-there-exist-a-n-and-b-n-all-integers-such-as-C-n-a-n-2-b-n-2-explicit-a-5-and-b-5-interm-of-a-and-b-

Question Number 90730 by ~blr237~ last updated on 25/Apr/20 $${let}\:{a}\:,{b}\:{integer}\:{and}\:\:{C}={a}^{\mathrm{2}} +{b}^{\mathrm{2}} \: \\ $$$${Prove}\:{that}\:{there}\:{exist}\:{a}_{{n}} \:{and}\:{b}_{{n}} \:{all}\: \\ $$$${integers}\:{such}\:{as}\:{C}^{{n}} ={a}_{{n}} ^{\mathrm{2}} \:+{b}_{{n}} ^{\mathrm{2}} \: \\ $$$${explicit}\:{a}_{\mathrm{5}}…

if-y-sin-msin-1-x-prove-that-1-x-2-y-n-2-2n-1-xy-n-1-m-2-n-2-y-n-0-

Question Number 90679 by MWSuSon last updated on 25/Apr/20 $${if}\:{y}={sin}\left({m}\mathrm{sin}^{−\mathrm{1}} {x}\right),\:{prove}\:{that}\:\left(\mathrm{1}−{x}^{\mathrm{2}} \right){y}_{{n}+\mathrm{2}} −\left(\mathrm{2}{n}+\mathrm{1}\right){xy}_{{n}+\mathrm{1}} +\left({m}^{\mathrm{2}} −{n}^{\mathrm{2}} \right){y}_{{n}} =\mathrm{0} \\ $$ Commented by MWSuSon last updated on…