"Find the derivatives of the functions. f(x)=e4x−5" solved and explained

Lennie Carroll

Answered question

2021-05-22

Find the derivatives of the functions.

f (x) = e^{4 x - 5}

faldduE

Skilled2021-05-23Added 109 answers

Recall the generalized rule for the derivative of exponential function:

\frac{d}{d x} [e^{u}] = e^{u} \frac{d u}{d x}

NSLIn this exercise, we want to find the derivative of

f (x) = e^{4 x - 5}

To make use of the rule, denote the argument of the exponential function by u, i.e.
u=4x-5
Using the rule from Step 1, we get:

f^{'} (x) = e^{u} \frac{d u}{d x} = e^{4 x - 5} \frac{d}{d x} (4 x - 5)} = 4

= 4 e^{4 x - 5}

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?