Question

derivar f(x)=8x^4-2x

Answer 1

PREGUNTA

Derivar f(x)=8x^4-2x

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SOLUCIÓN

♛ HØlα!! ✌

Para poder derivar esta función debemos recordar 2 propiedades fundamentales, las cuales son

                               $1. \boxed{\dfrac{d}{dx}[f(x)+g(x)] = \dfrac{d}{dx}[f(x)]+\dfrac{d}{dx}[g(x)]}\\\\\\2. \boxed{\dfrac{d}{dx}[f(x)]^n= n[f(x)]^{n-1}}\\\\\\3. \boxed{\dfrac{d}{dx}[af(x)]=a\dfrac{d}{dx}[f(x)]}, siendo \: a:cte$

Entonces en el problema

                              $f(x) = 8x^4-2x\\\\\mathrm{Nos \: piden \: \dfrac{d}{dx}[f(x)]}\\\\\mathrm{Aplicamos\: la \:primera\: propiedad}\\\\\dfrac{d}{dx}[f(x)] = \dfrac{d}{dx}(8x^4)-\dfrac{d}{dx}(2x)\\\\\\\mathrm{Aplicamos\: la \:tercera\: propiedad}\\\\\dfrac{d}{dx}[f(x)] = 8\left(\dfrac{d}{dx}(x^4)\right)-2\left(\dfrac{d}{dx}(x)\right)\\\\\\\mathrm{Aplicamos\: la \:primera\: propiedad}\\\\\dfrac{d}{dx}[f(x)] = 8(4x^{4-1})-2(1x^{1-1})\\\\\\\dfrac{d}{dx}[f(x)] =8(4x^3) - 2(x^0)$

                             $\dfrac{d}{dx}[f(x)] =32x^3 - 2(1)\\\\\\\boxed{\boxed{\boldsymbol{\dfrac{d}{dx}[f(x)] =32x^3 - 2}}}$