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y=(x+2)(x-1)2 differentiate in respect to x

Guest Jul 21, 2017
 #1
avatar+19653 
+2

y=(x+2)(x-1)2 differentiate in respect to x

 

\(y=(x+2)(x-1)^2 \\ y=(x+2)(x^2-2x+1) \\ y=x^3-2x^2+x+2x^2-4x+3 \\ y = x^3-3x+3\\ \mathbf{y' = 3x^2-3 }\)

 

laugh

heureka  Jul 21, 2017
 #2
avatar+92806 
+2

y=(x+2)(x-1)^2 differentiate in respect to x

 

Use product rule

 

y'=uv'+vu'

 

\(u=x+2   \qquad     v=(x-1)^2\\ u'=1 \qquad \quad v'=2(x-1)\)

 

\(\frac{dy}{dx}=(x+2)*2(x-1)+(x-1)^2*1\\ \frac{dy}{dx}=2(x+2)(x-1)+(x-1)^2\\ \frac{dy}{dx}=(x-1)[(2x+4)+(x-1)]\\ \frac{dy}{dx}=(x-1)[(3x+3)]\\ \frac{dy}{dx}=3(x-1)(x+1)\\ \frac{dy}{dx}=3(x^2-1)\\ \frac{dy}{dx}=3x^2-3\\\)

Melody  Jul 21, 2017

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