- IsTim

Express each function as a power with a rational exponent, and then differentiate. Express each answer using positive exponents. y=sqrt(2x-3x^5)

- schrodinger

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- IsTim

Well. I'm just doing the first part. I got 1/2(2-15x^4)^-1/2

- dumbcow

ok sqrt is same as exponent of 1/2
then apply chain rule to differentiate
good..wait don't change inside...multiply whole thing by derivative of inside

- dumbcow

\[(2-15x^{4})\frac{1}{2}(2x-5x^{3})^{-1/2}\]

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## More answers

- dumbcow

**typo 3x^5

- IsTim

In my textbook, it says: \[y=(2x-3x^5)^{1/2}\]

- dumbcow

?? yes that is original function right

- IsTim

No, the answer. Well, the first half that isn't dy/dx.

- dumbcow

oh yeah...sqrt is same as exponent of 1/2

- IsTim

But I don't know how to get \[dy/dx=(2=15x^4 )/(2\sqrt{2x-3x^5}\]

- IsTim

Also, why is their exponent positive, but ours is negative?

- dumbcow

same answer i posted....ours is negative because its in numerator, when you flip it to denominator the sign of exponent changes

- IsTim

Ok. I understand the first part. Thanks.
I'll call out if I need help on the second part.

- IsTim

Um, to find the derviative I use 1/2(2x−5x^3)−1/2 right.

- dumbcow

whoah ...um we were doing 2nd part (finding derivative this whole time) or at least thats what i was doing

- IsTim

Oh no! How do I do the first part?

- dumbcow

sqrt is same as exponent of 1/2

- IsTim

To get dy/dx=(2=15x^4)

- IsTim

/(22x−3x5−−−−−−−√

- IsTim

I guess I can't copy Latex....

- IsTim

dy/dx=(2=15x^4)/(2sqrt(2x−3x^5))

- IsTim

How do I figure that out?

- dumbcow

let me try this, part 1 is super easy all you are doing is rewriting it using rational exponents
\[\large \sqrt[n]{x} = x^{1/n}\]
\[\sqrt{2x-3x^{5}} = (2x-3x^{5})^{1/2}\]
part 2: find derivative using chain rule
u = 2x-3x^5
du = 2-15x^4
\[\frac{d}{du} u^{1/2} = \frac{1}{2}u^{-1/2} = \frac{1}{2\sqrt{u}}\]
multiply by du and substitute 2x-3x^5 back in for u
\[\rightarrow \frac{2-15x^{4}}{2\sqrt{2x-3x^{5}}}\]

- IsTim

How'd you get du = 2-15x^4?

- IsTim

@dumbcow When you have time...

- dumbcow

isn't that what you got in your very 1st post ^^ ??
anyway, its the derivative of 2x-3x^5 using power rule
\[\large \frac{d}{dx} x^{n} = n*x^{n-1}\]

- IsTim

Ok. thanks.

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