Posted by **Please help** on Thursday, October 14, 2010 at 3:16pm.

We have to find the first and second derivative of f(x)=x^(2/3)(6-x)^(1/3)

I have the first derivative as being

(4-x)/(x^(1/3)(6-x)^(2/3))

And that I know is right. The second derivative is -8/(x^(4/3)(6-x)^(5/3))

I did all the work but I am not getting the right answer... I looked it over but I dont know where I am going wrong... can someone do like the fisrt several lines? Or the whole thing... Thanks!

- College Calculus 1 -
**ANYONE THERE!**, Thursday, October 14, 2010 at 3:38pm
Is there anyone that can help me with this!!!!!!!!!!!!!! PLEASE!!!!!!

- College Calculus 1 -
**Anonymous**, Friday, October 15, 2010 at 12:19am
d/dx((6-x)^(1/3) x^(2/3))

| Use the product rule, d/dx(u v) = v ( du)/( dx)+u ( dv)/( dx), where u = (6-x)^(1/3) and v = x^(2/3):

= | x^(2/3) (d/dx((6-x)^(1/3)))+(6-x)^(1/3) (d/dx(x^(2/3)))

| Use the chain rule, d/dx((6-x)^(1/3)) = ( du^(1/3))/( du) ( du)/( dx), where u = 6-x and ( du^(1/3))/( du) = 1/(3 u^(2/3)):

= | (x^(2/3) (d/dx(6-x)))/(3 (6-x)^(2/3))+(6-x)^(1/3) (d/dx(x^(2/3)))

| The derivative of x^(2/3) is 2/(3 x^(1/3)):

= | (x^(2/3) (d/dx(6-x)))/(3 (6-x)^(2/3))+(2 (6-x)^(1/3))/(3 x^(1/3))

| Differentiate the sum term by term and factor out constants:

= | (x^(2/3) (d/dx(6)-d/dx(x)))/(3 (6-x)^(2/3))+(2 (6-x)^(1/3))/(3 x^(1/3))

| The derivative of 6 is zero:

= | (2 (6-x)^(1/3))/(3 x^(1/3))-(x^(2/3) (d/dx(x)))/(3 (6-x)^(2/3))

| The derivative of x is 1:

= | (2 (6-x)^(1/3))/(3 x^(1/3))-x^(2/3)/(3 (6-x)^(2/3))

d^2/dx^2(x^(2/3) (6-x)^(1/3)) = -(2 (6-x)^(1/3))/(9 x^(4/3))-(2 x^(2/3))/(9 (6-x)^(5/3))-4/(9 (6-x)^(2/3) x^(1/3))

- College Calculus 1 -
**Yussuf**, Saturday, October 16, 2010 at 8:22pm
The equation S= -16t^2 + v*t + k gives the height of the ball at any time, t in seconds, where “v” is the initial velocity (speed) in ft/sec and “k” is the initial height in feet (as if you were on top of a tower or building).

## Answer this Question

## Related Questions

- calculus - Find the first and second derivative - simplify your answer. y=x/4x+1...
- calculus - Please help with this. I need the first derivative of f(x)=4(x+...
- Applied Calculus - Find the first and second derivative of the function: x/(7x+...
- calculus - Please help with this. I submitted it below but no one responded. I ...
- Calculus - I need to find the second derivative of y=x(x-1)^1/2. I found the ...
- Calculus--> bobpursley - How do you get m=0? from taking the second ...
- Calculus - How would I go about finding the derivative of f(x)=ln(x)(7x-2)^3 ...
- calculus - Please help with this. I submitted it below and was asked to clarify ...
- Calculus - R=M^2(c/2-m/3) dR/dM=CM-M^2 I found the derivative. Now how would I ...
- Calc I - if f(t)=sqrt(4t+1) find f''(2) I got the first derivative to be: 1/2(4t...