3.6-3.9 Unit 3b

Question 1

what is the derivative of:
a. sinx
b. cosx
c. secx
d. cscx

Answer 1

a. cos x
b. -sinx
c. secx(tanx)
d. -cscx(cotx)

Question 2

what does sin/cos=
and cos/sin?

Answer 2

tan
cot

Question 3

how do you find the derivative of e^x?

Answer 3

e^x(whatever this argument is) stays the same and then you multiply the whole thing by the derivative of x (the argument/exponent)

Question 4

what is the derivative of:
a. lnx
b. log(subscriptb)x
c. b^x

Answer 4

a. 1/x(or what ever argument it is like if it what lnsinx the derivative would be 1/sinx
b. 1/xlnb
c. b^xlnb (b can be any number like if it was 3^x the derivative would be 3^xln3)

Question 5

General facts:
a. log(subscriptb)y = x. = ?
b. lnx =
c. 1/x^3 =
d. lne =
e. lne^a =
f. log(subscriptb)(b^x) =
g. log(subsciptb)b =
h. b^log(subscriptb)x =

Answer 5

a. b^x=y
b. log(e)x
c. x^-3
d. 1
e. a
f. xlog(subscriptb)b=x
g. 1
h. x (also applies to e^lnx =x)

Question 6

Some log rules for fun
a. log(xy) =
b. log(x/y) =
c. logx^y =

Answer 6

a. logx + logy
b. logx-logy
c. ylogx

Question 7

what is the derivative of:
a. h(x) = sec(7x)
b. f(x) = (sin^9(x))
c. y = sinx^9
d. 1.6^cosx

Answer 7

a. h’(x) = 7sec(7x)tan(7x)
b. first f(x) -> (sin(x))^9 then
f’(x) = 9(sinx)^8 (cosx)
c. y’ = 9x^8cos(x^9)
d. (1.6^cosx)(ln1.6)(-sinx)

Question 8

what is the derivative of:
a. sin^2x + cos^2(2x)
b. sin^2pi
c. lne

Answer 8

a. sin2x-4cos2xsin2x
b. 0
c. 0

Question 9

Some useful identities:
a. 2sinxcosx =
b. sin^2(a)+cos^2(a) =

Answer 9

a. sin2x
b. 1 (as long as the arguments (a) are the same)