অবকলনবিদ্যা
Differentiation of Algebraic Functions
- 1. ddx(c)=0
2. ddx(x)=1
3. ddx(u)=dudx
4. ddx(cu)=c dudx
5. ddx(u+v)=dudx+dvdx
6. ddx(uv)=u dvdx+v dudx
7. ddx(un)=nun−1 dudx
8. ddx(√u)=dudx2√u
9. ddx(uv)=v dudx−u dvdxv2
10. ddx(cv)=−c dvdxv2
11. dydx=1dxdy=dydu⋅dudx=dydudxdu
Differentiation of Logarithmic and Exponential Functions
- 1. ddx(logau)=dudxulna
2. ddx(logu)=loge dudxu=dudxuln10
3. ddx(lnu)=dudxu
4. ddx(au)=aulna dudx
5. ddx(eu)=eududx
6. ddx(uv)=vuv−1 dudx+uvlnu dvdx
Differentiation of Trigonometric Functions
- 1. ddx(sinu)=cosu dudx
2. ddx(cosu)=−sinu dudx
3. ddx(tanu)=sec2u dudx
4. ddx(cotu)=−csc2u dudx
5. ddx(secu)=secutanu dudx
6. ddx(cscu)=−cscucotu dudx
Differentiation of Inverse Trigonometric Functions
- 1. ddx(arcsinu)=dudx√1−u2
2. ddx(arccosu)=− dudx√1−u2
3. ddx(arctanu)=dudx1+u2
4. ddx(arccot u)=− dudx1+u2
5. ddx(arcsec u)=dudxu√u2−1
6. ddx(arccsc u)=− dudxu√u2−1
Differentiation of Hyperbolic Functions
- 1. ddx(sinhu)=coshu dudx
2. ddx(coshu)=sinhu dudx
3. ddx(tanhu)=sech2u dudx
4. ddx(cothu)=−csch2u dudx
5. ddx(sechu)=−sechutanhu dudx
6. ddx(cschu)=−cschucothu dudx
Differentiation of Inverse Hyperbolic Functions
- 1. ddx(arcsinh u)=dudx√u2+1
2. ddx(arccosh u)=dudx√u2−1
3. ddx(arctanh u)=dudx1−u2
4. ddx(arccoth u)=dudx1−u2
5. ddx(arcsech u)=− dudxu√1−u2
5. ddx(arccsch u)=− dudxu√1+u2
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