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Rate of Change Formula
(f(b)-f(a))/(b-a)
Definition of a Derivative Formula:
lim as h—> 0 of (f(a+h)-f(a))/h
Equation of the Tangent Line
(y-y1)=m(x-x1)
When does a Derivative Fail to Exist?
Discontinuity
Cusp/Corner
Vertical Tangent
The Power Rule
f,(x)=nx(n-1)
Derivative of Sin x
cos x
Derivative of cos x
-sinx
Derivative of ax
axln(a)
Derivative of ex
ex
Derivative of logax
1/xln(a)
Derivative of ln x and logex
1/x
Product Rule
h’(x)=f’g+g’f
Quotient Rule
h’(x)=(f’g-f’g)/g2
Derivative of Tan x
sec2x
Derivative of cot x
-csc2x
Derivative of sec x
tanxsecx
Derivative of csc x
-cotxcscx