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How do I Differentiate Roots?

ummyes

for example 4 root X how would i go about differentiating that?

Reply 1

RNQ

It is the same as 4x^(1/2).

Reply 2

Prokaryotic_crap

4\sqrt x

is the same as

4x^\frac{1}{2}

Reply 3

ummyes

so you just call it 4x^1/2 4 x 1/2 =2 2x^1/2 - ^1 =2x^-1/2

Reply 4

RNQ

That is correct :smile:

BTW: 2x^(-1/2) is the same as 2/(root x)

Reply 5

OllyThePhilosopher

Yes.

Reply 6

ashy

ummyes

so you just call it 4x^1/2 4 x 1/2 =2 2x^1/2 - ^1 =2x^-1/2

Yes, but please lean LaTeX. I can't be bothered to look at your working.

Reply 7

im so academic

so basically

5 root x = dx/dy = 5x^1/2

and

8x^1/2 = dx/dy = 8 root x?

Reply 8

Prokaryotic_crap

power of 1/2 is the same as sqaure root, power of 1/3 is the same as cube root, power of 1/4 is same as fourth toot etc

power of 3/2 is power of 3 then square root

basically take to the power of numerator and root denominator e.g.

a^\frac{b}{c}

cth\sqrt(a^b)

Reply 9

username160792

im so academic

so basically

5 root x = dx/dy = 5x^1/2

and

8x^1/2 = dx/dy = 8 root x?

No.

5 \sqrt{x} = 5x^\frac{1}{2}

You can rewrite

\sqrt{x}

as a power of x

x^\frac{1}{2}

If you were wondering;

5x^\frac{1}{2}

Unparseable latex formula:

\frac{dy}{dx} = \frac{5}{2}x^-^\frac{1}{2} = \frac{5}{2 \sqrt{x}}

Reply 10

lesliemnx33

so whats the deriviative of root x from first principles?

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