SOLUTION: Differentiate (find the derivative) of the function 2/(&#8730;x) + x/(&#8730;3) + 6(3&#8730;x <-- cube root over x), the answer should be 1/(&#8730;3) - 1/&#8730;(x^3)

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Question 185259: Differentiate (find the derivative) of the function 2/(√x) + x/(√3) + 6(3√x <-- cube root over x), the answer should be 1/(√3) - 1/√(x^3) - 2/(3√x^2) <-- cube root over x^2). Please show your steps.
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

Since we know that:

We can take the derivitive of each term of your function and just add them. First thing to do is put your functions in terms of fractional exponents using the rules:

and

Now take the derivitive using the Power Rule:

Look at the next term:

And then the last term:

Then put it all back together:

However, I would rationalize all the denominators:

John

SOLUTION: Differentiate (find the derivative) of the function 2/(&#8730;x) + x/(&#8730;3) + 6(3&#8730;x <-- cube root over x), the answer should be 1/(&#8730;3) - 1/&#8730;(x^3) - 2/(3&#8730

SOLUTION: Differentiate (find the derivative) of the function 2/(√x) + x/(√3) + 6(3√x <-- cube root over x), the answer should be 1/(√3) - 1/√(x^3) - 2/(3&#8730