Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers): (ax + b)n

Asked by Pragya Singh | 1 year ago |  239

##### Solution :-

Let f(x) = (ax + b)n. Accordingly,

f(x + h) = {a(x + h) + b}n = (ax + ah + b)n By first principle,

$$f'(x)=\lim\limits_{h \to 0}\dfrac{f(x+h)-f(x)}{h}$$

$$\lim\limits_{h \to 0}\dfrac{(ax+ah+b)-(ax+b)^n}{h}$$

(using binomial theorem)

(Terms containing higher degrees of h)

$$(ax+b)^n[\dfrac{na}{(ax+b)}+0]$$

$$na\dfrac{(ax+b)^n}{ax+b}$$

$$na(ax+b)^{n-1}$$

Answered by Abhisek | 1 year ago

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