Question

differentiate y=(4-3x)^9​

Answer 1

$y = {(4 - 3x)}^{9} \\ \\ \\ \frac{dy}{dx} = \frac{d}{dx} {(4 - 3x)}^{9} \\ \\ \\ \frac{dy}{dx} = \frac{d}{dx} {(4 - 3x)}^{9} \times \frac{d}{dx}(4 - 3x)$

As It is a Function of a Function!

Now differentiating :-

$\frac{dy}{dx} = \frac{d}{dx} {(4 - 3x)}^{9} \times \frac{d}{dx}(4 - 3x) \\ \\ \\ \\ \frac{dy}{dx} = 9 {(4 - 3x)}^{9 - 1} \times ( \frac{d}{dx}4 - \frac{d}{dx}3x) \\ \\ \\ \frac{dy}{dx} = 9 {(4 - 3x)}^{8} \times (0 - 3) \\ \\ \\ \\ \frac{dy}{dx} = 9 {(4 - 3x)}^{8}( - 3) \\ \\ \\ \frac{dy}{dx} =(- 27 {(4 - 3x)}^{8})$

The general Formula used is :-

$y = {x}^{n} \\ \\ \\ \frac{dy}{dx} = n {x}^{(n - 1)}$

Answer!!

Answer 2

Given expression $y=(4-3x)^9$

We need to differentiate the given expression

$\frac{d}{dx}y=\frac{d}{dx}(4-3x)^9\\\frac{dy}{dx}=9(4-3x)^8 \times 4\\\frac{dy}{dx}=36(4-3x)^8$

The differentiated value of the given expression is $36(4-3x)^8$

To learn more about Differentiation from the given link

https://brainly.in/question/6643303

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