How do you find the derivative of $2/sqrtx$ ?

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Answer 1 · 2015-06-03T21:02:28

One law of exponentials states that $a^(m/n)=root(n)(a^m)$ . Thus, we can rewrite the function as

$2/(x^(1/2))$

Also, another law states that $a^-n=1/a^n$

Thus, we can rewrite this again as $2x^(-1/2)$

Now, derivating the function:

$(dy)/(dx)=(-1/cancel(2))cancel(2)x^(-3/2)=-x^(-3/2)$

If you prefer, $-1/sqrt(x^3)$

How do you find the derivative of 2/sqrtx2/sqrtx?