# 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.

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.