Question

find derivative of (8sqrt(x)+(9/2root3(x)))^2

Answer 1

You have not supplied sufficient parentheses to render the expression unambiguous, that probably explains why you get different results from different sources.

Is it
(9/2)root3(x)
or
9/(2root3(x)) ?

Answer 2

its like 9/2(x)^1/3

Answer 3

It is still not clear to me if (x)^1/3 is with the numerator or the denominator.

I assume you are transcribing from a type-set fraction where the paretheses around the denominator are understood. When transcribing to a single line (as in this case), you will need to insert explicitely the parentheses around ALL denominators and numerators to avoid ambiguity.

Answer 4

its in denominator

Answer 5

So we're looking at find the derivative of the following expression:
y=(8*sqrt(x)+((9/2)/(x)^(1/3)))^2

Using the chain rule, we get
dy/dx
= 2(8*sqrt(x)+((9/2)/(x)^(1/3))) * d(8*sqrt(x)+((9/2)/(x)^(1/3)))/dx

By writing
=(8*sqrt(x)+((9/2)/(x)^(1/3)))^2
=8x^(1/2) + (9/2)x^(-1/3)
We can differentiate u using the power rule:
du/dx = 8(1/2)x^(-1/2) + (9/2)(-1/3)x^(-4/3)

So dy/dx
=2(8*sqrt(x)+((9/2)/(x)^(1/3)))*(8(1/2)x^(-1/2) + (9/2)(-1/3)x^(-4/3) )
=64+12x^(5/6)-(27/2)x^(-5/3)
after simplification.
Check my work.

Answer 6

is this the final answer?

Answer 7

Yes it is, but you should check my work to make sure you understand how this is done, and that I did not make a mistake.