Explained: "how to find the derivative of f(u)=9eu+20"

naivlingr

Answered question

2021-09-02

how to find the derivative of $f (u) = 9 e^{u} + 20$

Answer & Explanation

falhiblesw

Skilled2021-09-03Added 97 answers

Find the derivative of the following via implicit differentiation:
$\frac{d}{d} u (f (u)) = \frac{d}{d} u (20 + 9 e^{u})$
Using the chain rule, $\frac{d}{d} u (f (u)) = \frac{d f (u)}{d u} \frac{d u}{d u}$ , where $u = u and \frac{d}{d u} (f (u)) = f^{'} (u) :$
$(\frac{d}{d} u (u)) f^{'} (u) = \frac{d}{d} u (20 + 9 e^{u})$
The derivative of u is 1:
$1 f^{'} (u) = \frac{d}{d} u (20 + 9 e^{u})$
Differentiate the sum term by term and factor out constants:
$f^{'} (u) = \frac{d}{d} u (20) + 9 (\frac{d}{d} u (e^{u}))$
The derivative of 20 is zero:
$f^{'} (u) = 9 (\frac{d}{d} u (e^{u})) + 0$
Simplify the expression:
$f^{'} (u) = 9 (\frac{d}{d} u (e^{u}))$
Using the chain rule, $\frac{d}{d} u (e^{u}) = \frac{d e^{u}}{d u} \frac{d u}{d u}$ , where $u = u and \frac{d}{d u} (e^{u}) = e^{u}$ :
$f^{'} (u) = 9 e^{u} (\frac{d}{d} u (u))$
The derivative of u is 1:
$f^{'} (u) = 19 e^{u}$
Simplify the expression:
$f^{'} (u) = 9 e^{u}$
Simplify the expression:
Answer:
$= 9 e^{u}$

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