Réitigh (1+2x)^1/2 | Réiteoir Mata Microsoft

Difreálaigh w.r.t. x

Luacháil

Graf

Tráth na gCeist

Algebra

Fadhbanna den chineál céanna ó Chuardach Gréasáin

https://socratic.org/questions/what-is-the-limit-of-1-2x-1-x-as-x-approaches-infinity

https://socratic.org/questions/what-is-the-derivative-of-3-2x-1-2

https://math.stackexchange.com/questions/1297799/find-a-formula-for-the-binomial-coefficients-of-the-macluarin-series-for-frac

https://math.stackexchange.com/questions/82428/using-the-taylor-expansion-for-1x-1-2-evaluate-sum-n-0-infty-bi

https://math.stackexchange.com/questions/2954152/find-the-binomial-expansion-of-the-function-up-to-the-first-3-non-zero-terms-s

Roinn

Cóipeáladh go dtí an ghearrthaisce

\frac{1}{2}\left(2x^{1}+1\right)^{\frac{1}{2}-1}\frac{\mathrm{d}}{\mathrm{d}x}(2x^{1}+1)

Más F comhshuíomh dhá fheidhm indifreáilte f\left(u\right) agus u=g\left(x\right), is é sin, más F\left(x\right)=f\left(g\left(x\right)\right), mar sin is ionann díorthach F agus díorthach f maidir le u méadaithe faoi dhíorthach g maidir le x, is é sin, \frac{\mathrm{d}}{\mathrm{d}x}(F)\left(x\right)=\frac{\mathrm{d}}{\mathrm{d}x}(f)\left(g\left(x\right)\right)\frac{\mathrm{d}}{\mathrm{d}x}(g)\left(x\right).

\frac{1}{2}\left(2x^{1}+1\right)^{-\frac{1}{2}}\times 2x^{1-1}

Is ionann díorthach iltéarmaigh agus suim dhíorthaigh a théarmaí. Is ionann díorthach téarma thairisigh agus 0. Is ionann díorthach ax^{n} agus nax^{n-1}.

x^{0}\left(2x^{1}+1\right)^{-\frac{1}{2}}

Simpligh.

x^{0}\left(2x+1\right)^{-\frac{1}{2}}

Do théarma ar bith t, t^{1}=t.

1\left(2x+1\right)^{-\frac{1}{2}}

Do théarma ar bith t ach amháin 0, t^{0}=1.

\left(2x+1\right)^{-\frac{1}{2}}

Do théarma ar bith t, t\times 1=t agus 1t=t.