Question

Just started learning about derivatives and the chain rule. Chain rule confuses me, so... heres the problem.
f(x)=(5x^2-4x)^3
According to the chain rule,
f'(x)=(10x-4)*3*(5x^2-4x)^2
but according to my thinking...
n=5x^2-4x therefore,
f(x)=n^3 and f'(x)=3n^2
so... f'(x)=3(5x^2-4x)^2

Answer 1

yep but while differentiating n it is valid for n
but n is actually a quadratic in x which is also changing hence we use chain rule
learn limits u may understand derivatives better

Answer 2

f'(x)=(10x-4)*3*(5x^2-4x)^2 is correct.

if n = 5x^2-4x then the derivative of (n)^3 with respect to x (not n) will be 3* (dn/dx) * n^2

Answer 3

dn/dx = 10x-4, so in the end it's f'(x)=(10x-4)*3*(5x^2-4x)^2

Answer 4

what does (dn/dx) mean? like I said, I just started learning this stuff.

Answer 5

think of it like this
dx=dn*dx/dn

Answer 6

derivative of n wrt x