Derivatives + review

d/dx [c]?

(where c=any number)

0

d/dx (x^n)?

nx^(n-1)

d/dx [c times f(x)]?

c times f’(x)

Definition of a derivative

f’(x) = lim h→0 [f(x+h)-f(x)]/h

d/dx sinx?

cosx

d/dx cosx?

-sinx

d/dx [secx]?

secxtanx

d/dx [tanx]?

sec²x

d/dx [cotx]?

-csc²x

d/dx [cscx]?

-cscxcotx

d/dx [f times g]?

f’g + fg’ (product rule)

d/dx [f/g]?

[gf’-fg’]/g’

d/dx (lnx)?

1/x

how to turn square root into fraction

image

ln(x) = ?

log base e of x

log to exponential form

Image

how to solve logs?

ex) log base 3 of 27

how many 3’s do you need to multiply to get to 27?

log base 3 of 27 = 3

d/dx e^x?

e^x

d/dx e^(ct)?

c times e^(cx)

d/dx b^u

image

what is the chain rule for derivatives?

image

How to find derivatives of inverse trig functions?

(sin, cos, tan, sec)

sin^-1(u)? = u’/sqrt(1-u²)

cos^-1(u)? = -u’/sqrt(1-u²)

tan^-1(u) = u’/1+u²

sec^-1(u)= u’/[ |u| times sqrt(u²-1)]

how to go from exponent to square root?

image

Memorize the unit circle

image

how to turn decimal to fraction:

1. enter decimal

2. 2nd

3. PRB

4. 2nd

5. Ab/c