We are given:
Using the chain rule, we find:
hence:
Hi,
Would anyone be able to tell me how I'd go about solving a problem like this. Are you taking the derivative of the entire problem or just the one in the parenthesis (f(4x^3))? The inclusion of (f) is also throwing me off, not sure if that's supposed to be part of the solution. Is the answer supposed be something like = 12x^2(f'(4x^3))? Any help on this would be greatly appreciated. Thanks! Ana
Here's the problem . . .
d/dx(f(4x^3)) = 6x^5
Calculate f'(x) = ?
Just in case a picture helps...
... where (key in spoiler) ...
Spoiler:
_________________________________________
Don't integrate - balloontegrate!
Balloon Calculus; standard integrals, derivatives and methods
Balloon Calculus Drawing with LaTeX and Asymptote!
The question is related to single derivative function. solving it as:
(d(f(4x^3)/dx)=6x^5
=>3*4x^2.f'(4x^3)=6x^5
f('4x^3)=6x^5/12x^2
=>f'(4x^3)=x^3/2
=>f'(x)=x^3/(2*4x^2)
=>f'(x)=x/8
Derivative is defined as a measure of how a function changes as its input changes. This process of finding derivative is called differentiation.