Question

How to derive (ax+b)² ?

Answer 1

Like, deriving the expanded form of this binomial?

Answer 2

I think that ;
if we call U=x² and V=ax+b
Drive like that :
F'(x)=a*u'(V)

Answer 3

Ohh, derivatives. We could either differentiate term-by-term from the expanded form, or use chain rule.
Chain rule:
\( \displaystyle \frac{\text{d}}{\text{d}x} \left( (ax + b)^2 \right) \)
\( \displaystyle = \frac{\text{d} \left(ax+b\right)^2}{\text{d}x} \)
\( \displaystyle = \frac{\text{d} (ax + b)^2}{\text{d} (ax + b)} \times \frac{\text{d} (ax + b)}{\text{d}x} \)

Answer 4

d(ax+b)/dx = a
If we call U=x^2 and V = ax + b, then..
d(ax+b)^2/d(ax+b) = d(U(V))/dV = U'(V) seems correct to me.