Thread: 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) = 4t² - 12 + (4/t²)

F’(t) = (d/dt) (4t² -12 + (4/t²)

= 8t + 4t^-2

F’’(t) = (d/dt) (8t + 4t^-2)

= 8 – 8t^-1

F’’’(t) = (d/dt) (8 – 8t^-1)

= 8

Originally Posted by JDS

Compute the indicated derivative.
f'''(t) for f(t) = 4t² - 12 + (4/t²)

It is completely wrong.
Write as:
Then

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

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

bump

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).

Ive got a headache now, btw

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

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