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Get rid of the radicals.

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

right.. 3x^(11/2)

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

+ -4*x^-7/2 ?

Yes.

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

\[3x ^{\frac{ 11 }{ 2 }}-4x ^{\frac{ -7 }{ 2 }}\]
Now take the derivative.

14x/x^9/2

huh?

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

doesn't the x9/2 down

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

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

this is my work so far:

i have one question if you dont mind

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

i dont know why i always messed them up

i thought it would be like this:
= 6x^(1/2) then
=3x^(-1/2)
=3/(x^(1/2)

yes that is correct.