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

naivlingr

naivlingr

Answered question

2021-09-02

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

Answer & Explanation

falhiblesw

falhiblesw

Skilled2021-09-03Added 97 answers

Find the derivative of the following via implicit differentiation:
ddu(f(u))=ddu(20+9eu)
Using the chain rule, ddu(f(u))=df(u)dududu, where u=uandddu(f(u))=f(u):
(ddu(u))f(u)=ddu(20+9eu)
The derivative of u is 1:
1f(u)=ddu(20+9eu)
Differentiate the sum term by term and factor out constants:
f(u)=ddu(20)+9(ddu(eu))
The derivative of 20 is zero:
f(u)=9(ddu(eu))+0
Simplify the expression:
f(u)=9(ddu(eu))
Using the chain rule, ddu(eu)=deudududu, where u=uandddu(eu)=eu:
f(u)=9eu(ddu(u))
The derivative of u is 1:
f(u)=19eu
Simplify the expression:
f(u)=9eu
Simplify the expression:
Answer:
=9eu

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