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How do you differentiate #f(x)=e^(x^2+x+8) # using the chain rule?

1 Answer

May 4, 2018

#d/dx (e^(x^2+x+8)) = (2x+1)e^(x^2+x+8)#

Explanation:

Based on the chain rule, let #y(x) = x^2+x+8#, then:

#(df)/dx = (df)/dy dy/dx = d/dy (e^y) * d/dx (x^2+x+8)#

#(df)/dx = (df)/dy dy/dx =e^y (2x+1)#

#(df)/dx = (df)/dy dy/dx = (2x+1)e^(x^2+x+8)#

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