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Differentiating Exponential functions In Exercise,find the derivative of the function. See Example 2 and 3.
y = xex - 4e - x

Respuesta :

Answer: The derivative would be [tex]y'=e^x(1+x)+4e^{-x}[/tex]

Step-by-step explanation:

Since we have given that

[tex]y=xe^x-4e^{-x}[/tex]

as we know the product rule:

[tex]xe^x=x'e^x+xe^x'=e^x+xe^x[/tex]

so, it becomes,

[tex]y'=e^x(1+x)-4\times -1e^{-x}\\\\y'=e^x(1+x)+4e^{-x}[/tex]

Hence, the derivative would be

[tex]y'=e^x(1+x)+4e^{-x}[/tex]

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