Hello,
Please could someone run through deriving these 2 equations through algebraic expansion.
d/dx {sqrt(2y)}
and
d/dx {-1/((2x)^3)}
Thankyou in advance.
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?
Hello, euphmorning!
the first one . . .
So: .$\displaystyle \frac{d}{dx}\left[(2x)^{\frac{1}{2}}\right] $
. . . . $\displaystyle =\;\tfrac{1}{2}\cdot(2x)^{-\frac{1}{2}}{\color{red}\cdot 2} $
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.