Differentiating problem?

[Snicho1]

Hi there,

I tend to struggle with deriving things.
My question is to find the 1st and 2nd derivative of y= (x-2)^2/3 + 2

For the first derivative I pulled the 2/3 down in front and subtracted 1, so that I have 2/3(x-2)^-1/3. Not sure if I am on the right track? Or where I should go from here?

Thank You

 

[JeffM]

Hi there,

I tend to struggle with deriving things.
My question is to find the 1st and 2nd derivative of y= (x-2)^2/3 + 2

For the first derivative I pulled the 2/3 down in front and subtracted 1, so that I have (2/3)(x-2)^(-1/3). This is fine except you missed a mandatory (marked in red) and a helpful but not mandatory (marked in blue) pair of parentheses.

Not sure if I am on the right track? Yes

Or where I should go from here? Take the derivative of (2/3)(x - 2)^(-1/3).

Thank You

The second derivative is just a derivative. It follows the same rules as a first derivative.

The second derivative of a function is just the derivative of the function's derivative.

 

[lookagain]

Hi there,

I tend to struggle with deriving things.
My question is to find the 1st and 2nd derivative of y= (x-2)^(2/3) + 2 This is not fine. You missed mandatory grouping symbols around the exponent.

For the first derivative I pulled the 2/3 down in front and subtracted 1, so that I have (2/3)(x-2)^(-1/3). This is fine except you missed a mandatory (marked in red) and a helpful but not mandatory (marked in blue) pair of parentheses.

Not sure if I am on the right track? Yes

Or where I should go from here? Take the derivative of (2/3)(x - 2)^(-1/3).

Thank You :grin:


For the first derivative I pulled the 2/3 down in front and subtracted 1, so that I have (2/3)(x-2)^(-1/3). This is fine except you missed a mandatory (marked in red) and a helpful but not mandatory (marked in blue) pair of parentheses.

Not sure if I am on the right track? Yes

Or where I should go from here? Take the derivative of (2/3)(x - 2)^(-1/3).

Thank You :grin: