Find the 2nd Derivative - Basic Calc

[bobraymund]

Homework Statement

If g is a twice differentiable function and f(x) = xg(x^2), find f" in terms of g, g', and g".

Homework Equations

The Attempt at a Solution

I tried this with a lot of work, wouldn't be bothered to put it all here, and came up with:

f'' = (6x)*g'(x^2) + (4x^3)*g"(x^2)

Is this right or am I completely off? This question was confusing...

Is this even what they're asking for?

-Bob

 

[Avodyne]

Your answer is correct! Getting it involves repeated use of the chain rule and the product rule.

 

[bobraymund]

Your answer is correct! Getting it involves repeated use of the chain rule and the product rule.

Thanks!

I thought it looked like a weird answer so wasn't entirely sure.

Gracias,
Bob

 

[NastyAccident]

Homework Statement

If g is a twice differentiable function and f(x) = xg(x^2), find f" in terms of g, g', and g".

Homework Equations

The Attempt at a Solution

I tried this with a lot of work, wouldn't be bothered to put it all here, and came up with:

f'' = (6x)*g'(x^2) + (4x^3)*g"(x^2)

Is this right or am I completely off? This question was confusing...

Is this even what they're asking for?

-Bob

Yup, you are correct! I got: 4*x^3*g''(x^2)+6*x*g'(x^2).

As Avodyne said, "Getting it involves repeated use of the chain rule and the product rule."

So, you've just showed that you understand both of these concepts well!

Solve in terms, generally means solve the equation/formula with y on one side and x on the other side... So, you are making x independent of your equation/formula with y being dependent on x. IE: Think of the cartesian plane, (x,y) {(1,1), (2,2), (3,3), etc...}



NastyAccident