Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

**typo 3x^5

Answer 5

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

Answer 6

?? yes that is original function right

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

Oh no! How do I do the first part?

Answer 16

sqrt is same as exponent of 1/2

Answer 17

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

Answer 18

/(22x−3x5−−−−−−−√

Answer 19

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

Answer 20

dy/dx=(2=15x^4)/(2sqrt(2x−3x^5))

Answer 21

How do I figure that out?

Answer 22

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
\[\rightarrow \frac{2-15x^{4}}{2\sqrt{2x-3x^{5}}}\]

Answer 23

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

Answer 24

@dumbcow When you have time...

Answer 25

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

Answer 26

Ok. thanks.