Question

Differentiate the x the function :
(3x² - 9x +5²)

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Answer 1

Firstly , before solving the equation , we should know about the chain rule and its formula.

Formula For the Chain rule-

$\rightarrow$ $\sf\dfrac\pink{dy}\pink{dx}$=$\sf\dfrac\pink{dy}\pink{du}$ $\times$ $\sf\dfrac\pink{du}\pink{dx}$ $\leftarrow$

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$\sf\huge\underline{\underline{Question:}}$

$\sf\small{Differentiate\: x\: the \:function: (3x² - 9x + 5²)}$

$\sf\huge\underline{\underline{Solution:}}$

$\sf{Let\:y = (3x^2 - 9x + 5)^9}$

$\space$

☆ Differentiating both the sides w.r.t.x using chain rule-

$\mapsto$
`\sf(dy)/(dx)=`
`\sf(d)/(dx)`
`\sf{(3x^2 - 9x + 5)^9}`

$\space$

$\space$

$\mapsto$
`\sf(dy)/(dx)`=
`\sf{9(3x^2-9x+5)^8}`
`*`
`\sf(d)/(dx)`$\sf\small{(3x^2-9+5)}$

$\space$

$\space$

$\mapsto$
`\sf(dy)/(dx)`=
`\sf{9(3x^2-9x+5)^8}`
`*`
`\sf(6x-9)`

$\space$

$\space$

$\mapsto$
`\sf(dy)/(dx)`=
`\sf{9(3x^2-9x+5)^8}` $\times$
`\sf{3(2x-3)}`

$\space$

$\space$

$\mapsto$
`\sf(dy)/(dx)`=
`\sf{27(3x^2-9x+5)^8(2x-3)}`

$\space$

$\space$

$\sf\underline\bold\green{❍ dy:dx=27(3x^2-9x+5)^8(2x-3)}$

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