Let f be continuous on [a,b] and differentiable on (a,b) and if f(a)=f(b) then there is at least one number c on (a,b) such that f'(c)=0 (If the slope of the secant is 0, the derivative must = 0 somewhere in the interval).
Back
d/dx (x^2)
Front
2x
Back
d/dx (e^x)
Front
e^x
Back
Log A - Log B
Front
Log (A/B)
Back
d/dx (tan x)
Front
(sec x)^2
Back
Product rule
Front
d/dx (uv) = uv' + vu'
Back
Point-slope form of a line
Front
y-y1 = m (x-x1)
Back
d/dx (cos x)
Front
-sin x
Back
d/dx (x^3)
Front
3x^2
Back
k Log A
Front
Log (A^k)
Back
Log A + Log B
Front
Log (AB)
Back
d/dx (csc x)
Front
-(csc x)(cot x)
Back
d/dx (cot x)
Front
-(csc x)^2
Back
d/dx (ln x)
Front
1/x
Back
Mean Value Theorem
Front
If f is continuous on [a,b] and differentiable on (a,b), then there exists a number c on (a,b) such that f'(c)=(f(b)-f(a))/(b-a)