Differentiation Rules (Chapter 3) Flashcards
What is the d/dx of ex?
ex
What is the d/dx of cos x?
-sin x
How do you find the derivative of f at x?
Lim as delta x -> 0: f(x + delta x) - f(x) / delta x
What is the d/dx of eu?
euu’
What is the d/dx of ln x?
1 / x
What is the d/dx of logax?
1 / (ln a) * x
What is the d/dx of cos-1(u)?
-u’ / sqrt(1-u2)
What is the d/dx of sec-1(u)?
u’ / |u| * sqrt (u2-1)
What is the d/dx of |u|?
u / |u| * (u’)
What is the d/dx of tan x?
sec2x
What is the d/dx of ax?
(ln a) * ax
What is the formula for volume of a conic?
1/3(pi)r2h
What is the quotient rule ([d/dx] u / v)?
vu’ - uv’ / v2
What is the alternate definition of a limit? How can this be used to determine differentiability with absolute value?
f(x) - f(x) / x - c
Evaluate the limit at c+ and c-. If they differ, the function is not differentiable.
What is the d/dx of ax?
(ln a) ax
What is the chain rule ([d/dx] f(u))?
f’(u) * u’ for each function in the expression.
What is the d/dx of csc-1(u)?
-u’ / |u| sqrt(u2 - 1)
What is the d/dx of au?
(ln a) au * u’
What is the d/dx of sin x?
cos x
What is the product rule ([d/dx] u * v)?
uv’ + vu’
What is the simple power rule ([d/dx] xn)?
For xn, nxn-1.
For x1, 1.
What is the derivative of a constant?
0
What is the d/dx of sec x?
sec x tan x
What is the constant multiple rule ([d/dx] c*u)?
c * u’