# College Calculus 1

posted by .

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 don't know where I am going wrong... can someone do like the fisrt several lines? Or the whole thing... Thanks!

• College Calculus 1 -

Is there anyone that can help me with this!!!!!!!!!!!!!! PLEASE!!!!!!

• College Calculus 1 -

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 -

The equation S= -16t^2 + v*t + k gives the height of the ball at any time, t in seconds, where âvâ is the initial velocity (speed) in ft/sec and âkâ is the initial height in feet (as if you were on top of a tower or building).

## Similar Questions

1. ### Calculus

R=M^2(c/2-m/3) dR/dM=CM-M^2 I found the derivative. Now how would I find the vale of M that maximize the derivative dR/dM?
2. ### Calculus--> bobpursley

How do you get m=0? from taking the second derivative?
3. ### Calculus

How would I go about finding the derivative of f(x)=ln(x)(7x-2)^3 first=ln(x) second= (7x-2)^3 Would I do first times the derivative of the second + second times the derivative of the first?
4. ### calculus

Please help with this. I need the first derivative of f(x)=4(x+squareroot (x(8-x)) and then the second derivative of this to show by the second derivative test that it is a local maximum. This is difficult to put into form here and …
5. ### calculus

Please help with this. I submitted it below but no one responded. I need the first derivative of f(x)=4(x+ then the square root to include (x(8-x)), then close bracket.And then the second derivative of this to show by the second derivative …
6. ### calculus

Please help with this. I submitted it below and was asked to clarify by Henry (hope this is clearer and thank you). I need the first derivative of f(x)=4(x+ sqrt (x(8-x)).And then the second derivative of this to show by the second …
7. ### calculus

Find the first and second derivative - simplify your answer. y=x/4x+1 I solved the first derivative and got 1/(4x+1)^2 Not sure if I did the first derivative right and not sure how to do the second derivative.
8. ### Calculus

I need to find the second derivative of y=x(x-1)^1/2. I found the first derivative is 2x-1/2(x-1)^1/2, if someone could check, but I am miserably stuck on the second derivative.
9. ### Applied Calculus

Find the first and second derivative of the function: x/(7x+10) Using quotient rule. This is part of my homework in the section named "Higher Order Derivatives". I am confused on getting the second derivative, as I found the first …
10. ### math

For what intervals is g(x) = 1/x2 + 1 concave down?

More Similar Questions