Question

harsh basumatari is a cool twitter user.​

Answer 1

yes he is really a cool twitter user.

Answer 2

‌
${\fcolorbox{red}{blue}{\orange}{\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: SugarCrash\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:}}}$

$\\\huge\tt\pink{\underline{Question}} :$
$\large \bf To \: Differentiate \sf :- \sqrt{x} (x^3 + x^2 - 2x)​$

$\\\\\huge\tt\blue{\underline{Answer}} :$
$\implies\sf \large \tt \dfrac{1}{2\sqrt{x}}(7x^3+5x^2-9x)$
$\\\\ \huge\tt\blue{\underline{Solution}} :$

We know,
$\bf Derivative \: of \: \red{\boxed{UV = U\frac{d}{dy}V±V\frac{d}{dy}U}}$

Using this formula,
$\bf So, \sf \large derivative \: of \: \sqrt{x} (x^3 - x^2-3x)​ :- \\ \sf \sqrt{x}\frac{d}{dy}(x^3+x^2-3x)+(x^3+x^2-3x)\frac{d}{dy}(√x)$

$\\ \implies\large\sf \sqrt{x}(3x^2+2x-3)+(x^3+x^2-3x)\frac{1}{2}.(\sqrt{x})^{-1}$

$\implies \sf\large\sqrt{x}(3x^2+2x-3)+(x^3+x^2-3x)(\frac{1}{2\sqrt{x}})$

$\implies\sf\large \frac{1}{2\sqrt{x}}(x^3+x^2-3x+6x^3+4x^2-6x)$

$\implies \large \bf\pink{ \dfrac{1}{2\sqrt{x}}(7x^3+5x^2-9x)}$

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