How do you find the derivative of #e^(-3x)#?

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Answer 1 · 2018-06-18T07:47:41

#(dy)/(dx)=-3e^(-3x)#

#(dy)/(dx)=(dy)/(du)color(red)((du)/(dx))#

#y=e^(-3x)#

#color(red)(u=-3x=>(dy)/(du)=-3)#

#(dy)/(du)=d/(du)(e^u)=e^u#

#:.(dy)/(dx)=(dy)/(du)color(red)((du)/(dx))=e^uxxcolor(red)((-3))#

#=-3e^u=-3e^(-3x)#

in general:

#d/(dx)(e^(f(x)))=f'(x)e^(f(x))#

Answer 2 · 2018-06-22T07:35:17

#color(brown)(f'(x) = -3 e^-(3x)#

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

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

#f'(x) = e^(-3x) * (d/(dx)) (-3x)#

#f'(x) = e^-(3x) * -3#

#color(brown)(f'(x) = -3 e^-(3x)#