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Find the derivative of the following functions using first principles. a) f(x)= x^2 + 5^xQuestion
Find the derivative of the following function using First Principles.
f(x)= x^2+5^x
f(x)= x^2+5^x
Answers
Steve
the x^2 part is easy, right?
Now note that 5^x = (e^ln5)^x = e^(ln5 x)
Use google and you can find many sites which prove that the derivative of e^u = e^u using first principles. They all use some variation of the fact that
lim(n->0) (1 + 1/n)^n = e
Now note that 5^x = (e^ln5)^x = e^(ln5 x)
Use google and you can find many sites which prove that the derivative of e^u = e^u using first principles. They all use some variation of the fact that
lim(n->0) (1 + 1/n)^n = e