I need help with a complex derivative problem please

I need help finding the derivative of: f(x) = [ln(e^x)]^ 8 − ln[(e^x)^ 9]

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f(x) = [ln(e^x)]^ 8 − ln[(e^x)^ 9]        ← First simplify to something easier to differentiate

f(x) = [x ln(e)]⁸ − ln[(e⁹ᵡ)]
f(x) = [x ·1]⁸ − 9x ln(e)
f(x) = x ⁸ − 9x·1
f(x) = x ⁸ − 9x            ← Now, differentiate

f '(x) = 8x⁷ - 9            ← ANSWER


Have a good one!
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