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Find a complete set of derivative formulas
Derivation of compound function

F'(g(x))? =? [? F(g(x+dx))? -? F(g(x))? ]? /? dx? ( 1)?

g(x+dx)? -? g(x)? =? g'(x)*dx? =? dg(x)? (2)?

g(x+dx)? =? g(x)? +? dg(x)? (3)?

F'(g(x))? =? [? F(g(x)? +? dg(x))? -? F(g(x))? ]? /dx? =?

[? F(g(x)? +? dg(x))? -? F(g(x))? ]? /? dg(x)? *? dg(x)/dx? =?

f’(g)? *? g'(x)

Derivation formula of basic function

1.y=c(c is a constant)? y'=0?

2.y=x^n? y'=nx^(n- 1)?

3.y=a^x? y'=a^xlna?

y=e^x? y'=e^x?

4.y=logax? y'=logae/x?

y=lnx? y'= 1/x?

5.y=sinx? y'=cosx?

6.y=cosx? Sinks?

7.y=tanx? y'= 1/cos^2x?

8.y=cotx? y'=- 1/sin^2x?

9.y=arcsinx? y'= 1/√ 1-x^2?

10.y=arccosx? y'=- 1/√ 1-x^2?

1 1.y=arctanx? y'= 1/ 1+x^2?

12.y=arccotx? y'=- 1/ 1+x