# Thread: Problem:Calculus: Find derivative of [x (x+1) (x+2) (x+3)]^(1/3)

1. ## Problem:Calculus: Find derivative of [x (x+1) (x+2) (x+3)]^(1/3)

"I'm a college freshman in calculus, and we;re studying derivatives."

Q.Find the derivative of the following function:-
1)3th-rt(x(x+1)(x+2)(x+3)) .... this can be written as [x(x+1)(x+2)(x+3)](1/3)

My work:-

Webp.net-resizeimage.jpg

Webp.net-resizeimage (1).jpg

while i am stuck at a point where i have two options either 1)(x+2)(3x+1) 2)x(x+1)(x+1)(x+2) and none of it seems to be correct.
So,i need help in this part.

2. Originally Posted by manishpamnani169
"I'm a college freshman in calculus, and we;re studying derivatives."

Q.Find the derivative of the following function:-
1)3th-rt(x(x+1)(x+2)(x+3)) .... this can be written as [x(x+1)(x+2)(x+3)](1/3)

My work:-

Webp.net-resizeimage.jpg

Webp.net-resizeimage (1).jpg

while i am stuck at a point where i have two options either 1)(x+2)(3x+1) 2)x(x+1)(x+1)(x+2) and none of it seems to be correct.
So,i need help in this part.
If I were to do this problem I would start it this way:

d/dx{ [x(x+1)(x+2)(x+3)](1/3)}

=d/dx{ [x(1/3)] * [(x+1)(x+2)(x+3)](1/3)}

= [x(1/3)] * d/dx{[(x+1)(x+2)(x+3)](1/3)} + (1/3) * [x(-2/3)] * [(x+1)(x+2)(x+3)](1/3)

= [x(1/3)] * d/dx{[(x+1)(1/3)][(x+2)(x+3)](1/3)} + (1/3) * [x(-2/3)] * [(x+1)(x+2)(x+3)](1/3)

= [x(1/3)] * {[(x+1)(1/3)]d/dx{[(x+2)(x+3)](1/3) + (1/3) * [(x+1)(-2/3)]*[(x+2)(x+3)]} + (1/3) * [x(-2/3)] * [(x+1)(x+2)(x+3)](1/3)

and continue .... (be careful about those parentheses)

3. ## Thanks!!

Originally Posted by Subhotosh Khan
If I were to do this problem I would start it this way:

d/dx{ [x(x+1)(x+2)(x+3)](1/3)}

=d/dx{ [x(1/3)] * [(x+1)(x+2)(x+3)](1/3)}

= [x(1/3)] * d/dx{[(x+1)(x+2)(x+3)](1/3)} + (1/3) * [x(-2/3)] * [(x+1)(x+2)(x+3)](1/3)

= [x(1/3)] * d/dx{[(x+1)(1/3)][(x+2)(x+3)](1/3)} + (1/3) * [x(-2/3)] * [(x+1)(x+2)(x+3)](1/3)

= [x(1/3)] * {[(x+1)(1/3)]d/dx{[(x+2)(x+3)](1/3) + (1/3) * [(x+1)(-2/3)]*[(x+2)(x+3)]} + (1/3) * [x(-2/3)] * [(x+1)(x+2)(x+3)](1/3)

and continue .... (be careful about those parentheses)
Thanks for the reply i will definitely try it out!!