Derivatives of Exponential Functions with Base e

Question

Answer 1

d/dx(x^(-7)) = -7x^(-8) by the chain rule

d/dx(e^(-8x)) = -8e^(-8x) also by the chain rule, notably that d/dx (-8x) = -8 and d/dx(e^(x)) = e^(x)

thus

d/dx(x^(-7) + e^(-8x)) = -7x^(-8) - 8e^(-8x)