How do you differentiate # f(x)=e^sqrt(3x+x^2)# using the chain rule.?

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Answer 1 · 2018-05-13T01:46:00

the answer
#dy/dx=[[3+2x]*e^(sqrt(3x+x^2))]/[2sqrt(3x+x^2)]#

show below

#f(x)=e^sqrt(3x+x^2)#

suppose

#u=sqrt(3x+x^2)#

#(du)/dx=[3+2x]/[2sqrt(3x+x^2)]#

#y=e^u#

#dy/(du)=e^u#

#dy/dx=(du)/dx*dy/(du)#

#dy/dx=[3+2x]/[2sqrt(3x+x^2)]*e^u#

#dy/dx=[[3+2x]*e^(sqrt(3x+x^2))]/[2sqrt(3x+x^2)]#