Question

calculo 1 derivada y=x-2=

Answer 1

A derivada da soma/diferença é a soma/diferença das derivadas:

$\dfrac{d}{dx}[a(x)\pm b(x)\pm c(x)\pm ...\pm z(x)]=a'(x)\pm b'(x)\pm c'(x)\pm ...\pm z'(x)$

Derivada de potências de x:

$\dfrac{d}{dx}x^{n}=n\cdot x^{n-1}$

Derivada de constantes:

$\dfrac{d}{dx}k=0$
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$y=x-2\\\\y'=\frac{d}{dx}x-\frac{d}{dx}2\\\\y'=\frac{d}{dx}x^{1}-0\\\\y'=1\cdot x^{1-1}\\\\y'=1\cdot x^{0}\\\\y'=1\cdot1\\\\\boxed{\boxed{y'=1}}$

Se for pra achar a derivada pela definição:

$y'=\lim\limits_{\Delta x\rightarrow0}\dfrac{f(x+\Delta x)-f(x)}{\Delta x}\\\\\\y'=\lim\limits_{\Delta x\rightarrow0}\dfrac{([x+\Delta x]-2)-(x-2)}{\Delta x}\\\\\\y'=\lim\limits_{\Delta x\rightarrow0}\dfrac{x+\Delta x-2-x+2}{\Delta x}\\\\\\y'=\lim\limits_{\Delta x\rightarrow0}\dfrac{\Delta x}{\Delta x}\\\\\\y'=\lim\limits_{\Delta x\rightarrow0}1\\\\\\\boxed{\boxed{y'=1}}$