# Thread: Calculus Problems. Chain rule, rate of change.

1. ## Calculus Problems. Chain rule, rate of change.

Well I've been trying these problems for awhile, I'll type the problem out as well as what I have gotten as the answer and how I got there. Thanks for any help...my prof likes to throw things at us that is very challengin on HW..
PROBLEM 1
f(x)=1/(x-2x^2)^(9/8)
Find the derivative of f(x).

For starters i moved the binomial to the numerator and switched the power to negative giving me f(x)=(x-2x^2)^(-9/8) . After that I simply applied the chain rule giving me (-9/8)(x-2x^2)^-17/8(-4x) . It says this answer is incorrect...

PROBLEM 2
f(x)=sqrt(3+sqrt4x) The 4x has two sqrt over it. I broke this problem down to read f(x)=(3^1/2+4x^1/2)^1/2 . I then used the chain rule which gave me (1/2)(3^1/2+4x^1/2)(2x^-1/2) . It says this answer is incorrect...

I'll post the other two up after I get some help on these because I havent even been able to start them. They are more difficult then these two. Thanks for the help.

-Brad

2. Originally Posted by lmao
Well I've been trying these problems for awhile, I'll type the problem out as well as what I have gotten as the answer and how I got there. Thanks for any help...my prof likes to throw things at us that is very challengin on HW..
PROBLEM 1
f(x)=1/(x-2x^2)^(9/8)
Find the derivative of f(x).

For starters i moved the binomial to the numerator and switched the power to negative giving me f(x)=(x-2x^2)^(-9/8) . After that I simply applied the chain rule giving me (-9/8)(x-2x^2)^-17/8(-4x) . It says this answer is incorrect...
f(x)=1/[(x - 2x^2)^(9/8)] = (x - 2x^2)^(-9/8)

[(-9/8)*(x - 2x^2)^(-17/8)]*(1 - 4x)

The result you have is close; you didn't take the derivative of x, and remember that you're then multiplying that term by the whole expression.

3. Originally Posted by lmao
PROBLEM 2
f(x)=sqrt(3+sqrt4x) The 4x has two sqrt over it. I broke this problem down to read f(x)=(3^1/2+4x^1/2)^1/2 . I then used the chain rule which gave me (1/2)(3^1/2+4x^1/2)(2x^-1/2) . It says this answer is incorrect...

I'll post the other two up after I get some help on these because I havent even been able to start them. They are more difficult then these two. Thanks for the help.

-Brad
First of all, f(x)=(3^1/2+4x^1/2)^1/2 is not equivalent to f(x)=sqrt(3+sqrt4x). I think you mean:

(3 + (4x)^(1/2))^(1/2). Now this should be very easy.

[(1/2)*[3 + (4x)^(1/2)]^(-1/2)]*[[(1/2)*(4x)^(-1/2)]*4]

Voila.