Question

if f(z)=az+b and g(z)=cz+d, what are f'(z) and g'(z)

Answer 1

z is variable, a, b are constants

Answer 2

so that, take derivative respect to variable only

Answer 3

sorry all the z's are accually x's

Answer 4

doesn't matter, the same

Answer 5

I haven't done a derivative in 16 years I'm lost

Answer 6

want to re study or just the answer?

Answer 7

i need both

Answer 8

hahaha... ok
be patient, I will break it to baby steps. Ready?

Answer 9

go for it

Answer 10

(1)'=0
(2)'=0
(3)'=0......... so that if you have to take derivative of a number (so-called constant), the result =0 , got me?
now test, as above, I said that a, b is number, (b)' =?

Answer 11

knock, knock!! hard to understand or I gave you a preschool step? hahahaha ....

Answer 12

wow I think I lost it! I'm amazed I can't remember any of this

Answer 13

no need to remember any thing, I started a brand new lecture. hihihihii... read my comment and answer me (b)'=?

Answer 14

b'=0

Answer 15

Question: why do you have to take the course when you forgot all knowledge? This is the calculus1's stuff. The basis step of calculus.

Answer 16

yup!

Answer 17

now, variable: if x is variable, then (x)'= 1
if t is a variable, then (t)'=1
how about if y is a variable?

Answer 18

y'=1

Answer 19

yup again

Answer 20

now, if number* variable, and we have to take derivative of THEM, for example, 2x, it is 2*x and we just take derivative of the variable only, (2x)'=2 because x'=1 and 2*1 =2 right?
Now your turn (5y)'=?

Answer 21

y'=5

Answer 22

you miss 5 in the front of y', redo

Answer 23

so it's the slope

Answer 24

y'=1

Answer 25

5y'=?

Answer 26

=5

Answer 27

good, so, if a is number, x is variable and (a*x)' =?

Answer 28

=a

Answer 29

bingo

Answer 30

one more thing, sum of derivative = derivative of sum. That means (ax + b)' = (ax)' +b'
got me? so, (ax+b)'= ?

Answer 31

a+b

Answer 32

b is a number, and derivative of number is = ??

Answer 33

0

Answer 34

so, redo, (ax+b)'=

Answer 35

a

Answer 36

bingo,

Answer 37

now, look back your problem, f(x) = ax +b and they ask you find f'(x) =?

Answer 38

so in my question. f'(x)=a and g'(x)=c

Answer 39

WOAHH , you fired me??? hehehehe...

Answer 40

Congratulation, you got the correct answers

Answer 41

so if I add the functions together then find the derivatives what happens

Answer 42

particular one, please. You take the few baby steps, so that I dare not to say something without seeing the problem.

Answer 43

f(x)+g(x)=(ax+b)+(cx+d) find its derivative

Answer 44

Yes, exactly what we do, just add then take derivative. (the product and the quotient are not the same as sum and difference)

Answer 45

(a+c)

Answer 46

yup

Answer 47

if f(x) and g(x) are arbitrary functions what's the derivative of f(x)+g(x)?

Answer 48

if the degree of f and g is 1 as we did, then, do as we did
if the degree of f and g is not 1, then, you must study another thing.

Answer 49

Thank you so much. I will read on. I appreciate your help. Thank you!!!

Answer 50

for example, f(x) = 2x^3 -8x^2 +6 , you have to know how to take derivative of this function first. The degree of x is not 1

Answer 51

glad to help. good luck. Math is fun and beautiful. Win her!!