Urgent Maths Question! Please help me quick!!!?

Question

Could someone help me to find the derivative (gradient function) of:

f(x) = (((x^2 + 2x + 1) / 4) - 8) ^ (1/3)

Step by step working out please, but mainly the right answer!!

Please help me urgently.

One more question:

Radio-isotopes of different elements have different half-lives. Magnesium-27 has a half-life of 9.45 minutes. What is the decay constant for Magnesium-27? Round to five decimal places.

Please help me with the two questions urgently - if you cant help me with one, but you can help me with the other, that's absolutely fine! please help me especially with the first one.

thank you very much!

First person with the answer, I will choose as best answer!

Please quick!

Answer 1

[Note: quilasheila has missed a factor of 1/4...]

f(x) = (((x^2 + 2x + 1) / 4) - 8) ^ (1/3)
=> f'(x) = (1/3) (((x^2 + 2x + 1) / 4) - 8) ^ (-2/3) . d/dx (((x^2 + 2x + 1) / 4) - 8) by the chain & power rules
= (1/3) (((x^2 + 2x + 1) / 4) - 8) ^ (-2/3) . (1/4) d/dx (x^2 + 2x + 1) by the rules for constants (adding or multiplying)
= (1/3) (((x^2 + 2x + 1) / 4) - 8) ^ (-2/3) . (1/4) (2x + 2) by the power rule again.
= (1/6) (((x^2 + 2x + 1) / 4) - 8) ^ (-2/3) . (x + 1)

For the second question:
"Magnesium-27 has a half-life of 9.45 minutes. What is the decay constant for Magnesium-27? Round to five decimal places."
The decay constant is λ such that the equation for the number of particles remaining after time t is given by N(t) = N(0) e^(-λt). We know thet N(9.45) = 1/2 N(0), so we get
1/2 N(0) = N(0).e^(-λ(9.45))
so 9.45λ = ln 2
and hence λ = 0.07335 to 5 d.p.

Answer 2

f'(X) = 1/3(x^2 + 2x + 1) / 4) - 8) ^ (-2/3)
I wonder if I need to simplify

Formulae: dy/dx = nax^(n-1)

Answer 3

f(x) = (((x^2 + 2x + 1) / 4) - 8) ^ (1/3)

f ' (x) = (1/3) [ ((x^2 + 2x + 1) / 4) - 8 ] ^ (-2/3) * (2x+2)

Answer 4

this is your homework and you have to do it yrself.

if you just wanna to copy all the answer , why you study?

what can u learn?

Answer 5

sorry man i don't know