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Kryger [21]
3 years ago
7

Differentiate y=(r^2-9r)e^r

Mathematics
1 answer:
Alex Ar [27]3 years ago
7 0

Differentiate

y = (r² – 9r) · eʳ

with respect to  r.


As  y  is a product of two functions, then use the product rule:

 dy          d
——  =  —— [ (r² – 9r) · eʳ ]
 dr         dr

 dy          d                                                d
——  =  —— (r² – 9r) · eʳ  +  (r² – 9r)  ·  —— (eʳ)
 dr         dr                                               dr


•  The derivative of  r² – 9r  is  2r – 9;

•  The derivative of  eʳ  is  eʳ.


Therefore,

 dy                                               
——  =  (2r – 9) · eʳ  +  (r² – 9r) · eʳ
 dr 

 dy
——  =  [ (2r – 9) + (r² – 9r) ] · eʳ
 dr

 dy
——  =  (r² – 7r – 9) · eʳ   <———    this is the answer.
 dr


I hope this helps. =)

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