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Category: Differential Equation

Let-f-W-be-a-function-of-vector-W-R-N-i-e-f-W-1-1-e-W-T-x-Determine-the-first-derivative-and-matrix-of-second-derivatives-of-f-with-respect-to-W-

Question Number 203898 by necx122 last updated on 02/Feb/24 $${Let}\:{f}\left({W}\right)\:{be}\:{a}\:{function}\:{of}\:{vector}\:{W}\:\in\: {R}^{{N}} , \\ $$$${i}.{e}.\:{f}\left({W}\right)\:=\:\frac{\mathrm{1}}{\mathrm{1}\:+\:{e}^{−{W}^{{T}} {x}} } \\ $$$${Determine}\:{the}\:{first}\:{derivative}\:{and} \\ $$$${matrix}\:{of}\:{second}\:{derivatives}\:{of}\:{f}\:{with} \\ $$$${respect}\:{to}\:{W} \\ $$$$ \\…

Question-203694

Question Number 203694 by Numsey last updated on 26/Jan/24 Answered by Calculusboy last updated on 26/Jan/24 $$\boldsymbol{{Solution}}:\:\boldsymbol{{by}}\:\boldsymbol{{sub}}\:\boldsymbol{{directly}},\boldsymbol{{we}}\:\boldsymbol{{get}}\:\frac{\mathrm{0}}{\mathrm{0}}\left(\boldsymbol{{indeterminant}}\right) \\ $$$$\boldsymbol{{let}}\:\boldsymbol{\Delta}=\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\left(\mathrm{1}+\boldsymbol{{x}}\right)^{\mathrm{5}} }{\boldsymbol{{x}}^{\mathrm{2}} }−\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}} {\boldsymbol{{m}}}\frac{\boldsymbol{{e}}^{\mathrm{5}\boldsymbol{{x}}} }{\boldsymbol{{x}}^{\mathrm{2}} }+\boldsymbol{{li}}\underset{\boldsymbol{{x}}\rightarrow\mathrm{0}}…

Question-201555

Question Number 201555 by Simurdiera last updated on 08/Dec/23 Answered by mr W last updated on 09/Dec/23 $${let}\:{u}={x}+{y} \\ $$$$\frac{{du}}{{dx}}=\mathrm{1}+\frac{{dy}}{{dx}}\:\Rightarrow\frac{{dy}}{{dx}}=\frac{{du}}{{dx}}−\mathrm{1} \\ $$$$\Rightarrow\sqrt{{u}+\mathrm{1}}\left(\frac{{du}}{{dx}}−\mathrm{1}\right)=\sqrt{{u}−\mathrm{1}} \\ $$$$\Rightarrow\frac{{du}}{{dx}}=\frac{\sqrt{{u}−\mathrm{1}}}{\:\sqrt{{u}+\mathrm{1}}}+\mathrm{1} \\…

Question-200902

Question Number 200902 by Rupesh123 last updated on 26/Nov/23 Answered by Rasheed.Sindhi last updated on 26/Nov/23 $${f}\left({x}\right){f}\left({y}\right)+\mathrm{1}=\mathrm{2}{f}\left({xy}\right)+\mathrm{2}\left({x}+{y}\right) \\ $$$${x}={y}=\mathrm{1}: \\ $$$$\left[{f}\left(\mathrm{1}\right)\right]^{\mathrm{2}} +\mathrm{1}=\mathrm{2}{f}\left(\mathrm{1}\right)+\mathrm{4} \\ $$$$\left[{f}\left(\mathrm{1}\right)\right]^{\mathrm{2}} −\mathrm{2}{f}\left(\mathrm{1}\right)−\mathrm{3}=\mathrm{0}…

Question-200596

Question Number 200596 by Rupesh123 last updated on 20/Nov/23 Answered by witcher3 last updated on 22/Nov/23 $$\mathrm{a}\:\mathrm{True}\: \\ $$$$\mathrm{b}\:\mathrm{we}\:\mathrm{can}\:\mathrm{show}\:\mathrm{that}\:\mathrm{exist}\:\mathrm{bijection}\:\mathrm{between}\:\mathrm{som}\:\:\mathrm{set}\:\mathrm{of}\:\mathrm{not}\:\mathrm{differentiabl} \\ $$$$\mathrm{point}\:\mathrm{and}\:\mathbb{N}\: \\ $$$$ \\ $$…

Calculate-the-first-order-energy-correction-for-1-dimensional-non-degenerate-anharmonic-oscillator-whose-harmiltonian-is-HL-

Question Number 199996 by jlewis last updated on 12/Nov/23 $$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{first}\:\mathrm{order}\:\mathrm{energy}\:\mathrm{correction}\:\mathrm{for} \\ $$$$\mathrm{1}−\mathrm{dimensional}\:\mathrm{non}−\mathrm{degenerate}\:\mathrm{anharmonic} \\ $$$$\mathrm{oscillator}\:\mathrm{whose}\:\mathrm{harmiltonian}\:\mathrm{is}\:\mathscr{H}\underline{\mathscr{L}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

solve-the-associated-legendre-equation-l-l-1-2-l-0-1-2-and-m-2-l-l-1-which-requires-l-m-l-using-power-series-

Question Number 200022 by jlewis last updated on 12/Nov/23 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{associated}\:\mathrm{legendre}\:\mathrm{equation} \\ $$$$\lambda={l}\:\left({l}+\mathrm{1}\right)\eta^{\mathrm{2}} \:;{l}=\mathrm{0},\mathrm{1},\mathrm{2}…\:\:\:{and}\:{m}^{\mathrm{2}} \leqslant\:{l}\left({l}+\mathrm{1}\right)\: \\ $$$${which}\:{requires}\:−{l}\leqslant{m}\leqslant{l}\:\mathrm{using}\:\mathrm{power}\:\mathrm{series} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com