Wolfram Alpha Recall that given a function f we have defined

Wolfram Alpha

Recall that, given a function f we have defined the derivative function of f, written as f\'(x),by f\'(x) = lim h rightarrow 0 f(x +h) -f(x)/h For any specific value a, f\' (a) will represent the slope of the tangent line to the curve y = f(x) at the point (a, f(a)). We can use Wolfram Alpha (http v/www.wolframalpha.com/) to compute a formula for the derivative function for many common functions. For example, to find the derivative of 2^X, we simply tvpe in 1. Write down the result of executing this instruction below:

Solution

f(x) = 2^ x

f\'(x) = lt h-> 0 2^(x+h) - 2 ^x/(h)

f\'(x) = lt h-> 0 2^x *2 ^h - 2^x/h

f\'(x) = lt h-> 0  2^x(2 ^h -1)/h (lt h-> 0 (2 ^h -1)/h = log 2)

hence 2^x log2