How to find the derivative for these equations?

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Answer 1 · 2018-03-11T15:23:57

#-12e^(-4x)+e^x-2x#

Re-writing:

#3(e^x)^-4+e^x-x^2#

We know #dy/dxe^x=e^x#

Using the Chain Rule:

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

Letting #u=e^x#

#dy/dx(3(e^x)^-4+e^x-x^2)#

#= (-4)3(e^x)^-5*e^x+e^x-2x# *

#=-12e^(-4x)+e^x-2x#

*
#(e^x)^-5*e^x=e^(-5x+x)=e^(-4x)#