Calculate f'(3) to 3 significant figures where
f(t) = (4 t^2 + 3 t - 2 )^{-8}

Question

Calculate f'(3) to 3 significant figures where
f(t) = (4 t^2 + 3 t  - 2 )^{-8}

anonymous · Answer

i got -5.575356455*10^(-07) but it says i'm wrong

myininaya · Answer

So f(t)=(4 t^2 + 3 t - 2 )^{-8}
Did you apply the chain and power rule. 

f(t)=[g(t)]^n

f'(t)=n[g(t)]^(n-1)*g'(t)

myininaya · Answer

Also it kinda looks like you added 1 instead of subtracted 1 in the exponent area.

anonymous · Answer

yeah i forgot to subtract one for 3t, the new answer i got is -6.195008551*10^(-08) but i don't think it's right

myininaya · Answer

So can I see what you got for f'?

anonymous · Answer

-16*4^-8*t^-17+-8*3^-8*t^-9

phi · Answer

$$ (4 t^2 + 3 t  - 2 )^{-8}$$
using the rule
$$ \frac{d}{dx} x^n= n x^{n-1} dx $$
$$ -8 (4 t^2 + 3 t  - 2 )^{-8-1} d (4 t^2 + 3 t  - 2 )$$
you now have to take the derivative of the stuff in the parens
$$ -8 (4 t^2 + 3 t  - 2 )^{-8-1} (8 t^1 + 3  )$$

phi · Answer

$$ -8 (4 t^2 + 3 t  - 2 )^{-9} (8 t^1 + 3  ) $$

replace t with 3

anonymous · Answer

will it be -4.297715384*10^(-13)

phi · Answer

yes, but they want it rounded to 3 significant digits

anonymous · Answer

alright thanks

phi · Answer

I hope you got
-4.30 * 10^(-13)

anonymous · Answer

yes. another question.. for the derivative for sin^2(x), i got  2 sin (x) cos(x), but when i try to find f'(4) i got 0.139173101 but the system marks me wrong @phi

phi · Answer

I would guess that x is in radians.  make sure your calculator is in *radian mode* and not degree mode

anonymous · Answer

that helped.. thanks alot