Calc

• The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.
• The derivative of the function h(x) = e^x is e^x
• The derivative of the function g(x) = sin(x) is cos(x)
• The derivative of the function g(x) = ln x is 1/x
• The derivative of the function j(x) = csc(x) is -cot(x)
• The derivative of the function f(x) = csc(x) is -cot(x)
• The derivative of the function k(x) = sec(x) is tan(x)
• The derivative of the function m(x) = cot(x) is -csc(x)^2
• The derivative of the function n(x) = arcsin(x) is 1/(sqrt(1-x^2))
• The derivative of the function n(x) = cosec(x) is -tan(x)cosec(x)
• The derivative of the function m(x) = sec(x) is tan(x)sec(x)
• The derivative of the function k(x) = cot(x) is -csc^2(x)
• The derivative of the function n(x) = arctan(x) is 1/(1+x^2)
• The derivative of the function p(x) = arcsin(x) is 1/(sqrt(1-x^2))
• The derivative of the function m(x) = sec(x) is tan(x)sec(x)
• The derivative of the function o(x) = arccos(x) is -1/(sqrt(1-x^2))
• The derivative of the function o(x) = arccos(x) is -1/(sqrt(1-x^2))
• The derivative of the function q(x) = arcsec(x) is 1/(abs(x)*sqrt(x^2-1))
• The derivative of the function p(x) = arcsec(x) is 1/(abs(x)*sqrt(x^2-1))
• The derivative of the function o(x) = arccos(x) is -1/(sqrt(1-x^2))
• The derivative of the function q(x) = arcsec(x) is 1/(abs(x)*sqrt(x^2-1))
• Average rate of change is the secant line
• Average rate of change of a function is equal to (f[b] - f[a])/(b-a)
• the Intermediate value theorem is only applicable if f(x) is continuous and differentiable
• The mean value theorem is only applicable if f’(x) is continuous and differeable