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

Answer 1

Christopher Agresta

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)]#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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