Question

How do you differentiate `y=(e^(5x^4))/(e^(4x^2+3))`?

Answer 1

Rewrite as `y = e^(5x^4-4x^2-3)`, then use `d/dx(e^u) = e^u (du)/dx`

Explanation:

An important property of exponents is `a^n/a^m = a^(n-m)`

`y = e^(5x^4)/e^(4x^2+3) = e^(5x^4-4x^2-3)`

`y' = e^(5x^4-4x^2-3) * d/dx(5x^4-4x^2-3)`

`= (20x^3-8x)e^(5x^4-4x^2-3)`