Question

Derivative Question: Help (attached below)

Answer 1

Get rid of the radicals.

Answer 2

hint:\[ x^5\sqrt{x}=x^{5+\frac{1}{2}}=x^{\frac{11}{2}}\]

Answer 3

right.. 3x^(11/2)

Answer 4

That's it, and go with a negative exponent on the second term to avoid the quotient rule.

Answer 5

+ -4*x^-7/2 ?

Answer 6

Yes.

Answer 7

i got: 3x^(11/2)+14/x^9/2..

Answer 8

@NoelGreco

Answer 9

\[3x ^{\frac{ 11 }{ 2 }}-4x ^{\frac{ -7 }{ 2 }}\]

Now take the derivative.

Answer 10

14x/x^9/2

Answer 11

?

Answer 12

The derivative of the second term is\[\frac{ d }{ dx }3x ^{\frac{ 11 }{ 2 }}=\frac{ 33 }{ 2 }x ^{\frac{ 9 }{ 2 }}\]
I don't know how you're trying to take the derivative, but you simply use the power rule on each term.

Answer 13

huh?

Answer 14

from 3x^ (11/2) + 14x^(-9/2)

Answer 15

doesn't the x9/2 down

Answer 16

@NoelGreco hey sorry to interrupt. but i just needed to figure this out before leaving..

Answer 17

\[\frac{d}{dx}14x^{-\frac{9}{2}}=-\frac{9}{2}\times 14x^{-\frac{9}{2}-1}\]whatever that is

Answer 18

this is my work so far:

Answer 19

Before applying the power rule combine the terms as told you previously .
\[\Large f(x)=3x^5.x^\frac{1}{2}-\frac{-4}{x^3.x^\frac{1}{2}}\]

combining the terms
\[\Large f(x)=3x^\frac{11}{2}-\frac{4}{x^\frac{7}{2}}\]
\[\Large f(x)=3x^\frac{11}{2}-4x^{-\frac{7}{2}}\]

now Apply the Power rule.

Answer 20

thank you are you still there @sami-21

Answer 21

i have one question if you dont mind

Answer 22

what if they ask: derivative of sqrt(6x)

Answer 23

i dont know why i always messed them up

Answer 24

i thought it would be like this:

= 6x^(1/2) then
=3x^(-1/2)
=3/(x^(1/2)

Answer 25

@sami-21

Answer 26

yes that is correct.