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Limit definition Power rule Product rule Quotient rule Chain rule d/dx[e?]= d/dx[lnx]= d/dx[sin x] d/dx[tan x] d/dx[tan?¹x]= d/dx[cos x]= ∫kdx= ∫[f(x)±g(x)]dx= ∫1/x dx= ∫sinx dx= ∫sec²x dx= ∫cosx dx= ∫1/x²+a² dx=
- Limit definition
- Power rule
- Product rule
- Quotient rule
- Chain rule
- d/dx[e?]=
- d/dx[lnx]=
- d/dx[sin x]
- d/dx[tan x]
- d/dx[tan?¹x]=
- d/dx[cos x]=
- ∫kdx=
- ∫[f(x)±g(x)]dx=
- ∫1/x dx=
- ∫sinx dx=
- ∫sec²x dx=
- ∫cosx dx=
- ∫1/x²+a² dx=
Expert Solution
- Limit definition
f'(x)=f(x+h)-f(x)/h
- Power rule
d/dx[x?]=nx??¹
- Product rule
d/dx[f(x)g(x)]=f'(x)g(x)+f(x)g'(x)
- Quotient rule
d/dx [f(x)/g(x)]=f'(x)g(x)-g'(x)f(x)/[g(x)]²
- Chain rule
d/dx[f(g(x))]=f'(g(x))g'(x)
- d/dx[e?]=
e?
- d/dx[lnx]=
1/x
- d/dx[sin x]
cos x
- d/dx[tan x]
sec² x
- d/dx[tan?¹x]=
1/1+x²
- d/dx[cos x]=
-sin x
- ∫kdx=
kx+C
- ∫[f(x)±g(x)]dx=
∫f(x)dx±∫g(x)dx
- ∫1/x dx=
ln|x|+C
- ∫sinx dx=
-cos x+C
- ∫sec²x dx=
tan x+C
- ∫cosx dx=
sin x+C
- ∫1/x²+a² dx=
1/a tan?¹(x/a)+C
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