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Another way to look at this problem is to simplify the function first, then differentiate.
Depending on the teacher requirement, the answer can be simplified even more by rationalizing the denominator.
The function f(x)= `(x - 5*x*sqrt x)/sqrt x`
The derivative is determined using the quotient rule.
f'(x) = `[(x - 5*x*sqrt x)'*sqrt x - (x - 5*x*sqrt x)*(sqrt x)']/(sqrt x)^2`
=> `((1 - 5*(3/2)*sqrt x)*sqrt x - (1/2)*(x - 5*x*sqrt x)/sqrt x)/x`
=> `(sqrt x - (15/2)*x - (1/2)*sqrt x + (5/2)*x)/x`
=> `((1/2)*sqrt x - 5*x)/x`
=> `(1/2)/sqrt x - 5`
The derivative of `(x - 5*x*sqrt x)/sqrt x` is `1/(2*sqrt x) - 5`
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