Question

Differentiate :-
√x (x³ - x² -3x)​

Answer 1

$\\\huge\tt\blue{\underline{Question} :}$

$\large \sf To \: Differentiate : \\ \; \;\;\;\mapsto\;\;\; \bf \sqrt{x}(x^3 + x^2 -3x)$

$\\\\\huge\tt\blue{\underline{Answer} :}$

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

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

We know,

$\red\bigstar\bf \large Derivative \ of \red{ \boxed{\tt UV = U\frac{d}{dy}V+V\frac{d}{dy}U}}$

Using this formula,

$\bf So, \sf \large derivative \: of \: \sqrt{x}(x^3 + x^2 -3x) \\ \implies \sqrt{x}\dfrac{d}{dy}(x^3+x^2-3x)+(x^3+x^2-3x)\dfrac{d}{dy}(\sqrt{x} )$

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

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

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

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

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Answer 2

hola...
derivative of √x is 1/2×x^{-1/2}