Question

y=(3x²+7)(6x+7)

Hey mates plzz help me to solve this que. of diffrentiation​

Answer 1

here is ur ans.

diffrtin..w.r.t.x

dy/dx = d/dx (3x²+7)(6x+7)

=(3x²+7) d/dx (6x+7)+(6x+7)d/ dx (3x²+7)

dy/dx= (3x²+7).6+(6x+7)3.2x.

i think this will hlp u

Answer 2

$\huge\sf{\underline{Differeniation}}$

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$\sf{In\:above\:question\:we\:can\:easily\:find\:out\:that\:the\:terms\:are\:getting\:multiplied}$

$\huge{\mathfrak{Solution-}}$

$\sf{Formulae}$

Consider,

$(3 {x}^{2} + 7) \: as \: u \\ (6x + 7) \:as \: v$

So,

$d \frac{x}{y} = u \times d \frac{v}{x} + v \times d \frac{u}{x}$

$= > (3 {x}^{2} + 7) d\frac{(6x + 7)}{x} + (6x + 7)d \frac{(3 {x}^{2} + 7) }{x} \\ = > (3 {x}^{2} + 7)(6(1) + 0) + (6x+ 7)(2 \times 3) ({x})^{2 - 1} + 0) \\ = > (3 {x}^{2} + 7)(6) +(6x + 7)( {6}^{1} x) \\ = > {18}^{2} +42 + 36{x}^{2} + 42x \\ = > 54 {x}^{2} + 42x + 42$

$\boxed{\sf{54x2\:+42x\:+42}}$

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