Solve Derivative Question: f'(x) from d/dx (f(2x^4)) = 8x^5

[EvilBunny]

Homework Statement

If d/dx (f(2x^4)) = 8x^5

Calculate f'(x)

Homework Equations

The Attempt at a Solution

Well , we have been only doing derivatives for 2-3 class and its new for me.

From what I understand in this question is.

You have a function f(x) = something
The derivative of this function when you plug in 2x^4 gives you 8x^5
With that i suppose I should be able to find the equation of f(x) and then give f'(x) but I really don't know how to actually do this.

 

[ace123]

well are you finding the derivative of 2x^4 because if you are then it's not 8x^5. It's 8x^3. You use the power rule, which is x^n = nx^n-1

edit: If what your saying is correct then just work backwards from the power rule...

 

[EvilBunny]

Thats something diffrent the question is already saying

d/dx (f(2x^4) = 8x^5

 

[ace123]

I understand but if the derivative of a function is 8x^5 can you find the function?

 

[EvilBunny]

I guess am suppose to find the function but I don't know how. Am I suppose to take the power rule and use it in reverse or something of the sort

 

[ace123]

well i told you the power rule and you know what the derivative is going to be can't you work backwards to get to your function?

 

[EvilBunny]

ok so assuming we have to workd backwards the function of 8x^5 would be 1.6x^6

 

[ace123]

I don't think so b/c 6 times 1.6 will not give you 8...

 

[EvilBunny]

oh opps took the 5 instead yeah.

so 1.33 x ^ 6

 

[ace123]

okay so you have the function f(2x^4)= 4/3 x^6. Now you need to find f(x)

 

[pooface]

there could be numerous possibilities... if you are working backwards...because how will you find constants that equal to zero? they could be anything.
check the back of the book for the answer and see what it really wants.

To me I think it wants.
f(2x^4) = 8x^5 //compute this
Then take the derivative of 8(2x^4)^5.

 

[EvilBunny]

well its a work we do on the internet and the answers won't be submitted before some date so I guess I'll ask the teacher or other students next class but I still want to keep on trying for now

 

[ace123]

I agree with pooface b/c the way your really going about the problem just seems complicated for a class that has just started derivatives. Maybe the d/dx was a typo or you misread it. Then you would just do what pooface said by finding that derivative

 

[EvilBunny]

well in the whole 19 questions only 1-3 are like this. the others a basic , just apply the rules

 

[ace123]

Which is why i doubt they want you to do this complicated thing they probably just wanted you to sub the x with 2x^4 into 8x^5 and find the derivative

 

[EvilBunny]

well if I correctly did the derivative of 8(2x^4)^5 it gives me 45(2x^4)*8x^3

but the web thing says the answer is incorrect . wether I simpligy or not

 

[EvilBunny]

My teacher does like putting in nasty problems sometimes tho. Maybe that's it ? sometimes he writes soemthing partlially and says you will know how next week.

 

[ace123]

wouldn't your derivative be 5120x^19 not whatever you got

 

[pooface]

no that is not correct. (to evil bunny)

8*5 is 40 not 45.

Where is the exponent 5-1?

you can multiply the exponents out first if you like.