Video: Dab tsi yog qhov derivative ntawm Sinh 2x?
2024 Tus sau: Miles Stephen | [email protected]. Kawg hloov kho: 2023-12-15 23:36
Cov derivative ntawm sinh (u) sib (u) nrog rau kev hwm rau koj yog cosh(u) cosh (u). Hloov tag nrho qhov tshwm sim ntawm koj nrog 2x 2 x.
Ib yam li ntawd, tib neeg nug, dab tsi yog derivative ntawm Sinh?
Yog li, cov derivatives ntawm hyperbolic sine thiab hyperbolic cosine muaj nuj nqi yog muab los ntawm. ( sib x)'=(ex−e−x2)'=ex+e−x2=coshx, (coshx)'=(ex+e−x2)'= ex−e−x2= sib x.
Ib tug kuj yuav nug, dab tsi yog qhov derivative ntawm hyperbolic sine? Hyperbolic Muaj nuj nqi
| Muaj nuj nqi | Derivative | Daim duab |
|---|---|---|
| cosh(x) | sinh(x) | ↓ |
| tanh(x) | 1 - tanh(x)² | ↓ |
| coth(x) | 1-coth(x)² | ↓ |
| sech(x) | -sech(x)*tanh(x) | ↓ |
Hais txog qhov no, koj ua li cas sib txawv Cosh thiab Sinh?
Let g(x) = cosh x and h(x) = sib x 2, function f yog quotient ntawm functions g thiab h: f(x) = g(x) / h(x). Li no peb siv txoj cai quotient, f '(x) = [h(x) g '(x) - g(x) h '(x)] / h(x) 2, mus nrhiav derivative ua function f.
Tus qauv ntawm Sinhx yog dab tsi?
x = e x - e - x 2 sib x = dfrac{e^x - e^{-x}}{2} sib = 2 ex-e-x? coj? x = e x + e − x 2 cosh x = dfrac{e^x + e^{-x}}{2} coshx=2ex+e−x?
Pom zoo:
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