Find the derivative of y = (x^(6)-7x^(1.6))/√x
Apparently the answer is (11x^(11/9))/2-7.7x^(0.1) but I don't understand how you get the 2 for part of the answer in the 2-7.7x^(0.1)???
I would not say that "
2-7.7x^(0.1)" is part of the answer; by the order of operations, the 2 does not belong with the rest. Rather, the function is
\(\displaystyle y = \dfrac{x^6-7x^{1.6}}{\sqrt{x}}\)
and the derivative, as you state, is
\(\displaystyle y = \dfrac{11x^\frac{11}{9}}{2}-7.7x^{0.1}\)
where the 2 is in the denominator of the first term. The derivative could also be written as
\(\displaystyle y = \frac{11}{2}x^\frac{11}{9}-7.7x^{0.1}\)
I would start by simplifying the expression, writing the square root as a 1/2 power and then dividing each term in the numerator by that. Then take the derivative, and everything should fall into place.
I you still have trouble, you should show the main steps of your work, so we can see where you are going wrong.
