Posted by **isha** on Sunday, February 28, 2010 at 6:10pm.

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

- parentheses required -
**MathMate**, Sunday, February 28, 2010 at 7:13pm
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**, Sunday, February 28, 2010 at 7:19pm
its like 9/2(x)^1/3

- calculus -
**MathMate**, Sunday, February 28, 2010 at 7:34pm
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.

- calculus -
**Anonymous**, Sunday, February 28, 2010 at 7:42pm
its in denominator

- calculus -
**MathMate**, Sunday, February 28, 2010 at 8:23pm
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**, Sunday, February 28, 2010 at 9:17pm
is this the final answer?

- calculus -
**MathMate**, Sunday, February 28, 2010 at 9:42pm
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.

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