Calculus - Differentiation

Question

How would I differentiate this; Would it be quotient rule? The e in the numerator is throwing me off.

f(x) = e^3x / x⁴

Answer 1

Yes, you could use the quotient rule here, with the numerator function as e^3x, and the denominator as x⁴. Another option would be to rewrite the function with a negative exponent: f(x) = e^3x x^-4. You could then use the product rule. I personally prefer the second because then I don't have to remember the quotient rule. We would then differentiate:

f'(x) = 3e^3x(x^-4) + e^3x(-4x^-5)

This answer will definitely look different than what you would get using the quotient rule, but you can do a little algebraic manipulation to see that they are equivalent