Question

Differentiate (a^x)..?
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Answer 1

Step-by-step explanation:

Everyone used implicit differentiation so far. Works but I believe I can beat that. There is a pretty easy trick to differentiating a^x even easier ..

Answer 2

Answer:

$a^{x}$·ln(a)

Step-by-step explanation:

Let y = $a^{x}$

⇒ x = log y to the base a.

Differentiating both sides w.r.t x,

⇒ 1 = $\frac{1}{y \ ln(a)}$ · $\frac{dy}{dx}$

⇒ $\frac{dy}{dx}$ = y · ln(a)

As y = $a^{x}$, Substituting it in,

∴ $\frac{d}{dx} a^{x}$ = $a^{x}$·ln(a)

Hoping that I have not made any mistakes, You're welcome.

Hope you have found my answer useful. If my answer deserves a brainliest, do mark it.

GeniusH