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Calculus 180, Ch 3, S1-5
N/A
25
Mathematics
Undergraduate 1
10/26/2009
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Cards

Term
f'(c)=?
[The Constant Rule]
 Definition
0
Term
f'(x)=?
[The Identity Rule]
 Definition
1
Term
f'(x^n)=?
[The Power Rule]
 Definition
nx^(n-1)
Term
f'(1/x)=?
 Definition
-(1/x^2)
Term
What is the Normal Line?
 Definition
perpendicular to the tangent line and intersects the point that forms the tangent at the curve
Term
F'[cf(x)]=?
[The Constant Multiple Rule]
 Definition
cF'[f(x)]
Term
F'[f(x)+g(x)]=?
[The Sum Rule]
 Definition
F'[f(x)]+F'[g(x)]
Term
f'(e^x)=?
[The Exponential Rule]
 Definition
e^x
Term
F'[f(x)g(x)]=?
[The Product Rule]
 Definition
f'(x)g(x)+g'(x)f(x)
Term
F'[f(x)/g(x)]=?
[The Quotient Rule]
 Definition
[f'(x)g(x)-g'(x)f(x)]/[g(x)]^2
Term
lim as x->0 of [sinx/x]=?
 Definition
1
Term
lim as x->0 of [(cosx-1)/x]=?
 Definition
Term
f'(sinx)=?
 Definition
cosx
Term
f'(cosx)=?
 Definition
-sinx
Term
f'(tanx)=?
 Definition
(secx)^2
Term
f'(cscx)=?
 Definition
-cscxcotx
Term
f'(secx)=?
 Definition
secxtanx
Term
f'(cotx)=?
 Definition
(-cscx)^2
Term
f'(a^x)=?
["x" as the exponent]
 Definition
(a^x)lna
Term
f'(arcsinx)=?
 Definition
1/[sqrt(1-x^2)]
Term
f'(arctanx)=?
 Definition
1/(1+x^2)
Term
f'(arccosx)=?
 Definition
-1/[sqrt(1-x^2)]
Term
f'(arccscx)=?
 Definition
-1/[xsqrt(x^2-1)]
Term
f'(arcsecx)=?
 Definition
1/x[sqrt(x^2-1)]
Term
f'(arccotx)=?
 Definition
-1/(1+x^2)
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