Question

How do you differentiate `f(x)=x^2e^(x-1)` using the product rule?

Answer 1

`d/dxf(x)=x^2e^(x-1)+2xe^(x-1)`

Explanation:

From the product rule,
`d/dxuv=uv'+vu'`
`d/dxf(x)=d/dx(x^2e^(x-1))`
`d/dxf(x)=x^2*d/dxe^(x-1)+e^(x-1)*d/dxx^2`
`d/dxf(x)=x^2*e^(x-1)+e^(x-1)*2x`

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special note:
`d/dxe^(f(x))=d/dyf(x)*e^(f(x)`