Harlen Pritchard

2021-09-17

Find the derivatives

$y=({x}^{5}-2){(4x+3)}^{3}$

bahaistag

Skilled2021-09-18Added 100 answers

Step 1

The given function is

$y=({x}^{5}-2){(4x+3)}^{3}$

differentiate with respect to x

Step 2

$\frac{dy}{dx}=\frac{d}{dx}\left(({x}^{5}-2){(4x+3)}^{3}\right)$

$\frac{dy}{dx}=(({x}^{5}-2)\frac{d}{dx}{(4x+3)}^{3}+{(4x+3)}^{3}\frac{d}{dx}({x}^{5}-2))$

(using$\frac{d}{dx}u\cdot v=u\frac{d}{dx}v+v\frac{d}{dx}u$ )

$\frac{dy}{dx}=(({x}^{5}-2)\times 3{(4x+3)}^{2}\frac{d}{dx}(4x+3)+{(4x+3)}^{3}(5{x}^{4}-0))$

(using$\frac{d}{dx}{x}^{n}=n{x}^{n-1}$ )

$\frac{dy}{dx}=(({x}^{5}-2)\times 3{(4x+3)}^{2}\times 4+{(4x+3)}^{3}(5{x}^{4}-0))$

$\frac{dy}{dx}=12({x}^{5}-2){(4x+3)}^{2}+5{x}^{4}{(4x+3)}^{3}$ (answer)

The given function is

differentiate with respect to x

Step 2

(using

(using

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