# find derivative without using product//chain/or quotient rule..

• Jul 16th 2012, 05:34 PM
euphmorning
find derivative without using product//chain/or quotient rule..
Hello,

Please could someone run through deriving these 2 equations through algebraic expansion.

d/dx {sqrt(2y)}

and

d/dx {-1/((2x)^3)}

• Jul 16th 2012, 06:49 PM
euphmorning
Re: find derivative without using product//chain/or quotient rule..
edit ... just figured out the second one..
the first one I still can't get my head around!

i'll run through what i'm doing ..

so,

d/dx[2y]^1/2

= 1/2*[2y]^-1/2

= 1/2*(1/sqrt(2y)

=1/(2*sqrt(2y)) ....

i should be getting 1/sqrt(2y) ... where am i going wrong?
• Jul 16th 2012, 07:30 PM
Bean
Re: find derivative without using product//chain/or quotient rule..
Sqrt(2x)= sqrt(2)*sqrt(x)
• Jul 16th 2012, 07:56 PM
Soroban
Re: find derivative without using product//chain/or quotient rule..
Hello, euphmorning!

Quote:

the first one . . .

So: . $\frac{d}{dx}\left[(2x)^{\frac{1}{2}}\right]$

. . . . $=\;\tfrac{1}{2}\cdot(2x)^{-\frac{1}{2}}{\color{red}\cdot 2}$

• Jul 16th 2012, 08:08 PM
euphmorning
Re: find derivative without using product//chain/or quotient rule..
Heya, thanks for the responses.. i'm afraid I still can't see how to arrive @ 1/sqrt(2y)

:/
• Jul 16th 2012, 08:22 PM
Bean
Re: find derivative without using product//chain/or quotient rule..
The sqrt(2) is a constant so take the derivative of sqrt(x). 1/2(sqrt(x)). Multiply by the constant and arrive at sqrt(2)/2(sqrt(x)). Multiply that by sqrt(2)/sqrt(2) to get your answer.
• Jul 17th 2012, 01:18 AM
euphmorning
Re: find derivative without using product//chain/or quotient rule..
Got it at last, thankyou very much.