Compute the indicated derivative...just need guidance

I worked out my solution and was hoping for some input from the experts as to whether I did this correctly or not.

Thanks in advance!!

**Compute the indicated derivative.**

f'''(t) for f(t) = 4t^{2} - 12 + (4/t^{2})

F’(t) = (d/dt) (4t^{2} -12 + (4/t^{2})

= 8t + 4t^{-2}

F’’(t) = (d/dt) (8t + 4t^{-2})

= 8 – 8t^{-1}

F’’’(t) = (d/dt) (8 – 8t^{-1})

= **8**

Re: Compute the indicated derivative...just need guidance

Quote:

Originally Posted by

**JDS** **Compute the indicated derivative.**

f'''(t) for f(t) = 4t^{2} - 12 + (4/t^{2})

It is completely wrong.

Write as: $\displaystyle 4t^2-12+4t^{-2}$

Then

$\displaystyle 8t-8t^{-3}$

$\displaystyle 8+24t^{-4}$

$\displaystyle -96t^{-5}$

Re: Compute the indicated derivative...just need guidance

Wow, I don't know how I was so wrong! I think I need to go back and reread this chapter!!!

Re: Compute the indicated derivative...just need guidance

Okay, so lets see if I understand this now...., lets use the following:

Find the derivative:

f(x) = (x^3/2 - 4x) (x^4 - 3/x^2 +2)

then I would rewrite as........

= (x^3/2 -4x) (x^4 - 3x^-2 + 2)

then, take the derivative.......

f ' (x) = [((3/2 x^-3/2) - 4)(x^4 - 3x^-2 +2)] + [(x^3/2 - 4x) (4x^2 + 3x^-3)]

Ive got a headache now, btw :(

Re: Compute the indicated derivative...just need guidance

Re: Compute the indicated derivative...just need guidance

Quote:

Originally Posted by

**JDS** Okay, so lets see if I understand this now...., lets use the following:

Find the derivative:

f(x) = (x^3/2 - 4x) (x^4 - 3/x^2 +2)

then I would rewrite as........

= (x^3/2 -4x) (x^4 - 3x^-2 + 2)

then, take the derivative.......

f ' (x) = [((3/2 x^-3/2) - 4)(x^4 - 3x^-2 +2)] + [(x^3/2 - 4x) (4x^2 + 3x^-3)]

Not quite, though the errrors may be typos. The derivative of x^(3/2) is (3/2)x^(3/2- 1)= (3/2)x^(1/2), not (3/2)x^(-3/2),

the derivative of x^4 is 4x^(4- 1)= 4x^3, not 4x^2, and the derivative of 3x^(-2) is 3(-2)x^(-2-1)= -6x^(-3), not 3x^(-3).

Quote:

Ive got a headache now, btw :(

Don't worry, you'll get used to it!

Re: Compute the indicated derivative...just need guidance

Thanks! I've been pulling my hair out over this, lol!