Question

if (d/dx)(f(ax))=x² then f'(bx) =?​

Answer 1

Answers are given in the figure

Answer 2

we have first derivative of bx as

${f}^{1} (bx) = \frac{b}{a} ( {x}^{2} )$

Step-by-step explanation:

we know that

$\frac{d}{dx}(f (ax)) = {x}^{2} \\ implies \\ {f}^{1} (ax) = {x}^{2} \\ \\ which \: can \: be \: written \: as \\ a {f}^{1} (x) = {x}^{2} \: \: \: \: \: \: \: \\ {f}^{1}(x) = \frac{ {x}^{2} }{a} \: (equation \: 1)$

$\\ then \: to \: find {f}^{1} (bx) = b. {f}^{1} (x) \\ = b. {f}^{1} (x) \\ = b. \frac{ {x}^{2} }{a} \\ (from \: equation \: 1) \\ = \frac{b}{a} ( {x}^{2} )$

Definition

$\frac{d}{dx} (f( {x}) ) = {f}^{1} ( x) \\ {f}^{1} ( \alpha x) = \alpha . {f}^{1} (x)$

such that ,f(x) is a continuous function

$\alpha \: is \: any \: real \: number$

some other useful link related to this question

https://brainly.in/textbook-solutions/q-y-x-n-1-b-x-n-2

https://brainly.in/textbook-solutions/q-y-x-2-x-a-x-b-x-c-b-1

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