How do you differentiate #f(x) = 3x(e^((x-9)^2))^3# using the chain rule?

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Answer 1 · 2017-06-01T04:42:00

#e^((x-9)^6)(18x(x-9)^5+3)#

Step 1. Simplify the exponent

#f(x)=3x e^((x-9)^6)#

Step 2. Using the Product Rule directly uses the chain rule.

#f'(x)=3x d/dx(e^((x-9)^6))+e^((x-9)^6) d/dx(3x)#

#=3x e^((x-9)^6) d/dx((x-9)^6)+3e^((x-9)^6)#

#=3x e^((x-9)^6)(6(x-9)^5)+3e^((x-9)^6)#

#=18x(x-9)^5 e^((x-9)^6)+3e^((x-9)^6)#

Step 3. Factor out the common #e^((x-9)^6)# term

#=e^((x-9)^6)(18x(x-9)^5+3)#