I have been trying to do this question for like a week, and I have had no success.
Question:
Differentiate the function f(x)=(4x)/(sqrt2x)
I have tried it and I know that I have to use the quotient rule but I know I am doing something wrong in this step.
(2x)^1/2 * (4) - (4x) * (x)^-1/2 all divided by (2x)^3/2
Please help me do the multypling out.
Like Prove It, I recommend using negative powers and the product rule rather than positive powers and the quotient rule. However, since you specifically asked about that:
(2x)^1/2 * (4) - (4x) * (x)^-1/2 all divided by (2x)^3/2
You have a typo in the second term of the numerator: it should be [tex](2x)^{-1/2}[tex], not . Also the denominator is wrong. In the quotient rule, the quotient of the derivative is the square of the denominator of the function. Here, that is . You should have
To simplify that, factor out of the numerator.
so your numerator becomes .
Putting that into half power into the denominator makes it and, of course, .
You have a 3/2 power in the denominator after simplifying:
(Since the original problem was given in terms of the square root rather than a fractional power, it is probably better to give the answer that way.)