Skip to content

Latest commit

 

History

History
21 lines (17 loc) · 642 Bytes

2.3-标量:求导常用公式.md

File metadata and controls

21 lines (17 loc) · 642 Bytes

2.3-标量:求导常用公式

常用求导公式 $$(C)'=0$$ $$(x^a)' = ax^{a-1} a为实数$$ $$(a^x)' = a^x lna, (e^x)' = e^x$$ $$(log_ax)' = \frac{1}{xlna}, (ln|x|)' = \frac{1}{x}$$ $$(sinx)' = cosx$$ $$(cosx)' = -sinx$$ $$(tanx)' = \frac{1}{cos^2x}$$ $$(cotx)' = -\frac{1}{sin^2x}$$ $$(arcsinx)' = \frac{1}{\sqrt{1 - x^2}}$$ $$(arccosx)' = - \frac{1}{\sqrt{1 - x^2}}$$ $$(arctanx)' = \frac{1}{1 + x^2}$$ $$(\frac{e^x + e^{-x}}{2})' = \frac{e^x - e^{-x}}{2}$$ $$(\frac{e^x - e^{-x}}{2})' = \frac{e^x + e^{-x}}{2}$$ $$(ln(x + \sqrt{x^2 + 1}))' = \frac{1}{\sqrt{x^2 + 1}}$$ $$(ln(x + \sqrt{x^2 - 1}))' = \frac{1}{\sqrt{x^2 - 1}}$$