Question

Use the appropriate rules to determine teh derivitaive of....
i'll write teh equation below w/ teh equation tool

Answer 1

\[f(x) = 3x ^{5} - 2x ^{3/2} - (7/x ^{5}) + \sqrt{93}\]

Answer 2

well first thing to think of is that you can take the derivative of each term separately and then add them together.

Answer 3

so what's the derivative of 3x^5 to start?

Answer 4

well i have to do it first

Answer 5

isnt there a simpler way to do it with teh rules?

Answer 6

I'm using the rules: the derivate of a sum is the sum of the derivatives of the terms.

Answer 7

oh ok

Answer 8

anyway, you can use the rules to differentiate 3x^5

Answer 9

you subtract one from the power and multiply by the power: 5*3x^4

Answer 10

can u show me the steps?

Answer 11

to differentiate 3x^5 you multiply by the power of x, 5, and then subtract one from the power of x, so it becomes 5-1=4, so in total we have 5*3x^4

Answer 12

\[(ax^n)'=nax^{n-1}\]

Answer 13

a=3, n=5 in this case.

Answer 14

so its 3(5x^4) - 2(x^1/2) -..how about teh rest??

Answer 15

the derivative of the second term is -3x^(1/2)

Answer 16

-2*(3/2)=-3

Answer 17

so there are still two terms left to do.

Answer 18

ok

Answer 19

im not sure how to approach teh other 2

Answer 20

-(7/x^5)=-7x^-5

Answer 21

now you can do it just like before.

Answer 22

so taht will turn into -7(-5x^-6) or 35x^-6)

Answer 23

right

Answer 24

do i just leave teh sqrt of 93 or what do i do with it?

Answer 25

sqrt(93) is a constant, because there's no x in it, the derivative of a constant is zero.

Answer 26

oh ok
so so far i have:
f'(x) = 15x^4 - 3x^1/2 + 35x^-6

Answer 27

is taht the answer

Answer 28

that's right

Answer 29

tahnk you soo much!! can u help me with limits??

Answer 30

not now, sorry, I'm going to bed.

Answer 31

oh ok but thanks 4 ur help

Answer 32

You're welcome