How do you find the derivative of $y = a^{x}$ $y=a^x$ ?

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Answer 1 · 2015-04-15T14:23:00

For $a > 0$ $a > 0$ .

If you haven't memorized $\frac{d}{d x} (a^{x}) = a^{x} ln a$ $d/(dx)(a^x) = a^x lna$ , then you use

$y = a^{x} = e^{ln (a^{x})} = e^{x ln a}$ $y=a^x = e^(ln(a^x)) = e^(xlna)$ and differentiate using the chain rule to get:

$y' = e^(xlna) (lna) = a^x lna$

How do you find the derivative of y=a^xy=axy=a^x?