Question

In addition, can you walk me through how to get the derivatives for these 2 statements, too?

a) y = x^5/3 - 5x^2/3

b) y = (the cubed root of the quantity) [(x^2 - 1)^2]

Hi there. I need to find the first derivative of this statement.

y=x(x+2)^3

I tried the chain rule, but I think I messed up because I got y'=3(x+2)^5.

The reason I know it's wrong is because I'm trying to sketch the curve and my points are not where they should be.

Help?

Use primarily the product rule

y = x(x+2)^3

y' = (1)(x+2)^3 + x(3)(x+2)^2
=(x+2)^2(1+3x)

for your second post
a) y'=(5/3)x^(2/3) - (10/3)x^(-1/3)

b) y = [(x^2-1)^2]^(1/3)
= (x^2-1)^(2/3)
then y'=(2/3)(x^2-1)^(-2/3)(2x) etc

Thanks so much!