If f(x)=(ax+b)n,(x>−ba), then f|(x) is

A
$a n {(a x - b)}^{n - 1}$
B
$a n {(a x + b)}^{n + 1}$
C
$a n {(a x + b)}^{n - 1}$
D
$a n {(a x - b)}^{n + 1}$

Solution:

$\begin{array}{l} Write u = a x + b so that f (x) = u^{n} \\ Then f^{|} (x) = \frac{d}{d u} (u^{n}) . \frac{d u}{d x} \\ = n u^{n - 1} . a = a n {(a x + b)}^{n - 1} \end{array}$

If $f (x) = {(a x + b)}^{n}, (x > \frac{- b}{a})$ , then $f^{|} (x)$ is

Solution:

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