Calculate f'(x) given d/dx(f(3x^4))=6x^4?

  • Thread starter Thread starter firegoalie33
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on calculating the derivative f'(x) given the equation d/dx(f(3x^4))=6x^4. By applying the chain rule, it is established that f'(3x^4)(12x^3) equals 6x^4. This leads to the conclusion that f'(3x^4) can be derived by isolating it in the equation, resulting in f'(3x^4) = 6x^4 / (12x^3). Furthermore, substituting u = 3x^4 allows for the determination of f'(u).

PREREQUISITES
  • Understanding of the chain rule in calculus
  • Familiarity with differentiation techniques
  • Knowledge of function notation and derivatives
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Study the application of the chain rule in calculus
  • Explore examples of implicit differentiation
  • Learn about higher-order derivatives and their applications
  • Investigate the relationship between functions and their derivatives
USEFUL FOR

Students studying calculus, educators teaching differentiation, and anyone seeking to deepen their understanding of derivative calculations.

firegoalie33
Messages
2
Reaction score
0
I am told that d/dx(f(3x^4))=6x^4. I need to calculate f ' (x). i have tried like 3 different methods and have no idea how to do this.
Help please!
 
Physics news on Phys.org
Can you find f'(3x4)?
 
By the chain rule,
[tex]\frac{df(3x^4)}{dx}= f'(3x^4)(12x^3)[/tex]

So you must have [itex]f'(3x^4)(12x^3)= 6x^4[/itex].

That let's you find [itex]f'(3x^4)[/itex] per Office Shredder's question. Now, if you let [itex]u= 3x^4[/itex], you can find f'(u).
 

Similar threads

Verify Green's Theorem in the given problem
  • · Replies 10 ·
Replies
10
Views
2K
Find the local maxima and minima for##f(x,y) = x^3-xy-x+xy^3-y^4##
  • · Replies 5 ·
Replies
5
Views
1K
Find ##f(x)## in the problem involving integration
  • · Replies 3 ·
Replies
3
Views
1K
Find the second derivative of the relation; ##x^2+y^4=10##
  • · Replies 24 ·
Replies
24
Views
3K
How Do You Simplify and Analyze Taylor Polynomials for Higher Degree Functions?
  • · Replies 5 ·
Replies
5
Views
2K
Shine Bright: Solving the Equation \sinh 3x = 4\sinh^3x + 3 \sinh x
  • · Replies 5 ·
Replies
5
Views
2K
Question on Two Differentiation Techniques
  • · Replies 25 ·
Replies
25
Views
2K
How do I differentiate the function F(x)=4^{3x}+e^{2x}?
  • · Replies 5 ·
Replies
5
Views
2K
Chain Rule W/ Composite Functions
  • · Replies 4 ·
Replies
4
Views
1K
Computing line integral using Stokes' theorem
  • · Replies 8 ·
Replies
8
Views
2K