calculus

posted by .

I need help simplifying this problem.

f(x)=x^4/5(x-4)^2

f'(x)=x^4/5*2(x-4)+(x-4)^2*4/5x^-1/5

it is suposed to end up as this:

1/5x^-1/5(x-4)[5*x*2+(x-4)*4]

but how do i get it to there? I need to see all the steps and how to get them. Thanks

• calculus -

now, do you notice x^(-1/5) and x^(4/5) ?

isn't x^(-1.5) the highest common factor ? (just like a^4 would be the HCF for a^4 and a^6)

also (x-4) is a common factor,
as well as -1/5 (pretend your first term was (5/5)x^4/5*2(x-4)

so
(-1/5)(x^(-1/5)(x-4)[10 + 4(x-4)]

= (-1/5)(x^(-1/5)(x-4)[4x-6]
= (-2/5)(x^(-1/5)(x-4)[2x-3]

• calculus -

prove that sin invers (1/5)+COT INVERSE (3)=0

Similar Questions

2. Math

I need help simplifying radicals. The problem in priticular is the square root of 60x^2 √60x^2 can be simplified this way: √(4 * 15 * x^2) Can you see what to take out from under the square root sign?
3. Math

Solve for x: 5/x+6+2/x^2+7x+6=3/x+1 5/x+5+2/(x+6)(x+1)=3/x+1 5(x+6)(x+1)/x+6+2(x+6)(x+1)/(x+6)(x1)=3(x+6)(x+1)/x+1 5(x+1)+2=3(x+6) 5x+5+2=3x+18 5x+7=3x+18 2x=11 x=11/2 or 5 1/2 is my method correct?
4. math

how do u divide fractions? i really need help with this. i need to know all the steps. plese post the steps.i really need them before 9 oclock tonight. please help. thank u very much...

Okay, I just need the steps for simplifying this type of radical: 5 -- 3√2 thats all one problem. thanks!
6. Algebra Help

Okay, I just need the steps for simplifying this type of radical: 5 -- 3√2 thats all one problem. thanks!
7. Math

Okay, I just need the steps for simplifying this type of radical: 5 -- 3√2 thats all one problem. thanks!
8. College Algebra

I need some help with a handful of questions. I need to see the steps on how to get to the final answers. I would also appreciate if you can explain how you got to those steps. Rationalize each expression by building perfect nth root …