differentiation f(x)=xe^(5x), f'(x)=(1/5)

[skyblue]

differentiation f(x)=xe^(5x), f'(x)=(1/5)


ok so i got 5xe^5x + e^5x

now what do i do with the (1/5).
and is my differentiation correct?

 

[dora]

Hello, Skyblue!

You have done the differentiation correctly. The next step is to evaluate f' at x = 1/5. You have:

. . .f'(x) = 5 x e^5x + e^5x

Now plug "1/5" in for "x":

. . .f'(1/5) = 5 * (1/5) e^{(5 * (1/5))} + e^{(5 * (1/5))} = (1) e⁽¹⁾ + e⁽¹⁾ = e¹ + e¹ = 2e

If this isn't clear, please reply with your questions. Thank you!