How do you differentiate f(x)= 1/(e^(3x) -5x)f(x)=1e3x5x using the quotient rule?

1 Answer
Mar 3, 2018

(5-3e^(3x))/( e^(3x) - 5x)^253e3x(e3x5x)2

Explanation:

The quotient Rule states that
the derivative of a division of two functions f(x)/g(x)f(x)g(x)
Is equal to (f'(x)g(x) - f(x)g'(x))/ (g(x))^2

therefore in your Question,
let f(x) = 1
and g(x) = e^(3x) - 5x

their respective derivatives are
f'(x) = 0
g'(x) = 3e^(3x) - 5

therefore, the derivative of the entire equation using the Quotient rule is
((0*e^(3x) - 5x) - (1*(3e^(3x) - 5)))/ ( e^(3x) - 5x)^2

= - (3e^(3x) - 5)/( e^(3x) - 5x)^2

which is equal to
(5-3e^(3x))/( e^(3x) - 5x)^2
=
and you can simplify it more if you want but that's basically it