derivatives Flashcards
power rule
anx^n-1
derivative of sin x
cos x
derivative of cos x
-sin x
derivative of e^x
e^x
product rule
g(x) * f’(x) + g’(x) * f(x)
derivative of tan x
sec^2(x)
derivative of cot (x)
- csc^2(x)
derivative of sec x
sec x * tan x
quotient rule f(x)/g(x)
g(x) * f’(x) - g’(x) * f(x) / g^2(x)
catchy phrase to remember quotient rule
lo d hi - hi d lo over lo lo
derivative of csc x
-(csc x * cot x)
chain rule f(u(x)
= f’(u(x) * u’(x)
dertivative of y^2 (remember implicit differentiation)
2y * dy/dx
derivative of ln x
1/x
derivative of log x (base = b)
1/((ln b) * x)
derivative of b^x
b^x * ln b
derivative of arcsin x
1/√(1-x^2)
derivative of arccos x
-1/√(1-x^2)
derivative of arctan
1/(x^2 + 1)
definition of derivatives (using limmits)
lim h -> 0, (f(x+h) - f(x))/h
derivative of arccot
-1/(x^2 + 1)
derivative of arcsec
1/(|x|√(x^2 - 1))
derivative of arcsc
-1/(|x|√(x^2 - 1))
tangent line equation
y-y1 = m (x - x1)
normal line equation (perpendicular to tangent line)
same as tangent line but m = -1/m
