Derivatives Flashcards
What is the constant rule for derivatives?
d/dx [c] = 0
What is the power rule for derivatives?
Power rule is used for functions of the form x^n.
What is the derivative of an exponential function?
d/dx[a^x] = a^x * lna
What is the derivative of the natural exponential function?
d/dx[e^x] = e^x
What is the derivative of the sine function?
d/dx[sinx] = cosx
What is the derivative of the cosine function?
d/dx[cosx] = -sinx
What is the derivative of the tangent function?
d/dx[tanx] = sec^2x
What is the derivative of the cotangent function?
d/dx[cotx] = -csc^2x
What is the derivative of the secant function?
d/dx[secx] = secxtanx
What is the derivative of the cosecant function?
d/dx[cscx] = -cscxcotx
What is the derivative of the arcsine function?
d/dx[arcsinx] = 1 / sqrt(1 - x^2)
What is the derivative of the arccosine function?
d/dx[arccosx] = -1 / sqrt(1 - x^2)
What is the derivative of the arctangent function?
d/dx[arctanx] = 1 / (1 + x^2)
What is the derivative of the arccotangent function?
d/dx[arccotx] = -1 / (1 + x^2)
What is the derivative of the arcsecant function?
d/dx[arcsecx] = 1 / (|x| * sqrt(x^2 - 1))
What is the derivative of the arccosecant function?
d/dx[arccscx] = -1 / (|x| * sqrt(x^2 - 1))
How do you calculate the average rate of change over an interval [a,b]?
[f(b) - f(a)] / (b - a)
What is the instantaneous rate of change?
It is the derivative of the average rate of change.
