Trig Function Derivatives
Derivative of sin(x)
cos(x)
Derivative for arcsin(x)
1/(1-x^2)^1/2
What does a derivative represent?
Slope of the tangent line/specific point
x^5
4x^4
Derivative of cos(x)
-sin(x)
Derivative for arccot(x)
-1/(1+x^2)
Define Continuity rule (what are the steps?)
The limit and function both exist, and they are equal to each other.
4x^3
12x^2
Derivative of tan(x)
sec^2(x)
1/(1+x^2)
Name 3 types of discontinuities
Hole, jump, asymptote
x^-2
-2/x^3
Derivative of sec(x)
sec(x)tan(x)
Derivative for cosh(x)
sinh(x)
What does IVT prove?
A solution exists
1/sqrt(x)
1/2x^3/2
Derivative of cot(x)
-csc^2(x)
Derivative for arccsc(x)
-1/(x(x^2-1)^1/2)
What is the equation for solving derivatives by limit definition
(f(x-h)-f(x))/h as h approaches 0
5x^3/2-1/x
15sqrt(x)/2+1/x^2