00:01
In this problem, the first question is to determine the derivative of the function y is equal to 9 times square root of x divided by x.
00:08
Now, this function can be also written as y is equal to 9 times x -rays to 1 by 2 divided by x by using properties of radicals.
00:20
Now, by properties of exponents, we have a raise to m divided by a raise to n is equal to a raise to m minus n.
00:27
And using this we can rewrite this function as 9 x raise to half minus 1 which simplifies to 9x raise to negative half.
00:46
Now we can find the derivative d .y by dx for this function.
00:52
Now the derivative d .y by dx of this function can be obtained.
00:56
Using the equation the derivative d by d x of a function x raised to n can be determined as n x raised to n minus 1.
01:04
So using this we have the derivatives 9 times negative half times x raised to negative half minus 1 which simplifies to negative 9 by 2 x raised 2 negative 3 by 2.
01:20
And this can be also written as negative 9x divided by 2...