Posted by isha on .
find derivative of (8sqrt(x)+(9/2root3(x)))^2

parentheses required 
MathMate,
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)) ? 
calculus 
isha,
its like 9/2(x)^1/3

calculus 
MathMate,
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 typeset 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. 
calculus 
Anonymous,
its in denominator

calculus 
MathMate,
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. 
calculus 
Anonymous,
is this the final answer?

calculus 
MathMate,
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.