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would the derivative of f(x)=(7^x)(x^7) be f'(x)=(7^x ln7) (7x^6)?

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no, you have to use the product rule

f(x) = (7^x)(x^7)

f ' (x) = (7^x)(7x^6) + (x^7)(ln7)(7^x)
= (7^x)(x^6) (7 + x ln7)

ok thanks!
Also, how did you simplify it to (7^x)(x^6) (7 + x ln7) ?

I took out the highest common factor

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