Question

Differentiate a' w.r.t. x, where a is a positive constant.​

Answer 1

Answer:

Let us solve it by applying the definition of the derivative of a function ;

For y = f(x) = a^(x)

(dy/dx) = lim(h—->0) [f(x + h) - f(x)/h] or here

= lim [{a^(x + h) - a^x} /h ] ( h — −>0)

=(a^x) lim [{a^(h) - 1}/h] (h →0)

= a^(x) ln(a) (as lim{(a^h - 1)/h} = ln(a)).